03_modelFitting_testingBetaLASSO

Based on code from Martin Holdrege’s Sagebrush-Fire paper

The data consists of vegetation % cover by functional group from across CONUS (from AIM, FIA, LANDFIRE, and RAP), as well as climate variables from DayMet, which have been aggregated into mean interannual conditions accross multiple temporal windows.

Dependencies

Set user defined parameters

print(params)

## $run
## [1] FALSE
## 
## $save_figs
## [1] TRUE
## 
## $ecoregion
## [1] "noTrees"
## 
## $response
## [1] "TotalHerbaceousCover"
## 
## $removeTexasLouisianaPlain
## [1] FALSE
## 
## $removeAllAnoms
## [1] FALSE
## 
## $trimAnomalies
## [1] TRUE
## 
## $autoKfold
## [1] FALSE
## 
## $whichSecondBestMod
## [1] "auto"

# set to true if want to run for a limited number of rows (i.e. for code testing)
test_run <- params$test_run
save_figs <- params$save_figs
response <- params$response
fit_sample <- TRUE # fit model to a sample of the data
n_train <- 5e4 # sample size of the training data
n_test <- 1e6 # sample size of the testing data (if this is too big the decile dotplot code throws memory errors)
trimAnom <- params$trimAnomalies
removeTLP <- params$removeTexasLouisianaPlain
run <- params$run
autoKfold <- params$autoKfold
removeAllAnoms <- params$removeAllAnoms
whichSecondBestMod <- params$whichSecondBestMod

Load packages and source functions

# set option so resampled dataset created here reproduces earlier runs of this code with dplyr 1.0.10
source("../../../Functions/glmTransformsIterates.R")
source("../../../Functions/transformPreds.R")
source("../../../Functions/betaLASSO.R")

#source("../../../Functions/StepBeta_mine.R")
#source("src/fig_params.R")
#source("src/modeling_functions.R")
 
library(betareg)
library(ggspatial)
library(terra)
library(tidyterra)
library(sf)
library(caret)
library(tidyverse)
library(GGally) # for ggpairs()
library(pdp) # for partial dependence plots
library(gridExtra)
library(patchwork) # for figure insets etc. 
library(ggtext)
library(StepBeta)
theme_set(theme_classic())
library(here)
library(rsample)
library(kableExtra)
library(glmnet)
library(USA.state.boundaries)

Read in data

Data compiled in the prepDataForModels.R script

here::i_am("Analysis/VegComposition/ModelFitting/03_modelFitting_testingBetaLASSO.Rmd")

# get data that already have 
modDat <- readRDS( here("Data_processed", "CoverData", "CoverModelData_withTreeNoTreePreds.rds")) %>% st_drop_geometry()

# change Level 1 cover variables to be between 0 and 1 rather than 0 and 100
modDat[,"TotalTreeCover"] <- modDat[,"TotalTreeCover"]/100
modDat[,"TotalHerbaceousCover"] <- modDat[,"TotalHerbaceousCover"]/100
modDat[,"BareGroundCover"] <- modDat[,"BareGroundCover"]/100
modDat[,"ShrubCover"] <- modDat[,"ShrubCover"]/100

# For all response variables, make sure there are no 0s add  .0001 from each, since the Beta model framework can't handle that
modDat[modDat$TotalTreeCover == 0 & !is.na(modDat$TotalTreeCover), "TotalTreeCover"] <- 0.0001
modDat[modDat$TotalHerbaceousCover == 0  & !is.na(modDat$TotalHerbaceousCover), "TotalHerbaceousCover"] <- 0.0001
modDat[modDat$BareGroundCover == 0 & !is.na(modDat$BareGroundCover), "BareGroundCover"] <- 0.0001
modDat[modDat$ShrubCover == 0 & !is.na(modDat$ShrubCover), "ShrubCover"] <- 0.0001
modDat[modDat$AngioTreeCover_prop == 0 & !is.na(modDat$AngioTreeCover_prop), "AngioTreeCover_prop"] <- 0.0001
modDat[modDat$ConifTreeCover_prop == 0 & !is.na(modDat$ConifTreeCover_prop), "ConifTreeCover_prop"] <- 0.0001
modDat[modDat$C4GramCover_prop == 0 & !is.na(modDat$C4GramCover_prop), "C4GramCover_prop"] <- 0.0001
modDat[modDat$C3GramCover_prop == 0 & !is.na(modDat$C3GramCover_prop), "C3GramCover_prop"] <- 0.0001
modDat[modDat$ForbCover_prop == 0 & !is.na(modDat$ForbCover_prop), "ForbCover_prop"] <- 0.0001

# For all response variables, make sure there are no values of 1 -- subtract .0001 from each, since the Beta model framework can't handle that
modDat[modDat$TotalTreeCover == 1 & !is.na(modDat$TotalTreeCover), "TotalTreeCover"] <- 0.9999
modDat[modDat$TotalHerbaceousCover == 1  & !is.na(modDat$TotalHerbaceousCover), "TotalHerbaceousCover"] <- 0.9999
modDat[modDat$BareGroundCover == 1 & !is.na(modDat$BareGroundCover), "BareGroundCover"] <- 0.9999
modDat[modDat$ShrubCover == 1 & !is.na(modDat$ShrubCover), "ShrubCover"] <- 0.9999
modDat[modDat$AngioTreeCover_prop == 1 & !is.na(modDat$AngioTreeCover_prop), "AngioTreeCover_prop"] <- 0.9999
modDat[modDat$ConifTreeCover_prop == 1 & !is.na(modDat$ConifTreeCover_prop), "ConifTreeCover_prop"] <- 0.9999
modDat[modDat$C4GramCover_prop == 1 & !is.na(modDat$C4GramCover_prop), "C4GramCover_prop"] <- 0.9999
modDat[modDat$C3GramCover_prop == 1 & !is.na(modDat$C3GramCover_prop), "C3GramCover_prop"] <- 0.9999
modDat[modDat$ForbCover_prop == 1 & !is.na(modDat$ForbCover_prop), "ForbCover_prop"] <- 0.9999

Prep data

Identify the ecoregion and response variable type to use in this model run (i.e. trees or no trees)

ecoregion <- params$ecoregion
response <- params$response
print(paste0("In this model run, the ecoregion is ", ecoregion," and the response variable is ",response))

## [1] "In this model run, the ecoregion is noTrees and the response variable is TotalHerbaceousCover"

Visualize the predictor variables

The following are the candidate predictor variables for this ecoregion:

if (ecoregion == "noTrees") {
  # select potential predictor variables for the ecoregion of interest
        prednames <-
          c(
"tmean"         , "prcp"              , "prcp_dry"      , "prcp_seasonality"      ,"prcpTempCorr"     ,"isothermality" ,       
"clay"          , "coarse"            , "carbon"        , "AWHC"                  ,"tmin_anom"        ,"tmax_anom"   ,         
"t_warm_anom"   , "prcp_wet_anom"     , "precp_dry_anom", "prcp_seasonality_anom" ,"prcpTempCorr_anom","isothermality_anom",   
"annWatDef_anom", "annWetDegDays_anom", "VPD_min_anom"  , "frostFreeDays_anom")
  
} else if (ecoregion == "trees") {
  # select potential predictor variables for the ecoregion of interest
  prednames <- 
    c(
"tmean"             , "prcp"          , "prcp_dry"          , "prcpTempCorr"          ,"isothermality"    , "annWatDef" ,           
"sand"              , "coarse"        , "carbon"            , "AWHC"                  ,"tmin_anom"        , "tmax_anom" ,       
"t_warm_anom"       , "prcp_wet_anom" , "precp_dry_anom"    , "prcp_seasonality_anom" ,"prcpTempCorr_anom", "aboveFreezingMonth_anom",
"isothermality_anom", "annWatDef_anom", "annWetDegDays_anom", "VPD_min_anom"  
)
} else if (ecoregion == "CONUS") {
  prednames <- c(
"tmean"         , "prcp"              , "prcp_seasonality"    , "prcpTempCorr"      , "isothermality"           ,"annWetDegDays" ,         
"sand"          , "coarse"            , "AWHC"                , "tmin_anom"         , "tmax_anom"               ,"prcp_anom",         
"t_warm_anom"   , "precp_dry_anom"    , "prcp_seasonality_anom", "prcpTempCorr_anom",  "aboveFreezingMonth_anom", "isothermality_anom",
"annWatDef_anom", "annWetDegDays_anom", "VPD_min_anom"           
  )
} 

Scale the predictor variables for the model-fitting process

modDat_1 <- modDat 
allPreds <- modDat_1 %>% 
  dplyr::select(tmin:frostFreeDays,tmean_anom:frostFreeDays_anom, soilDepth:AWHC) %>% 
  names()
modDat_1_s <- modDat_1 %>% 
  mutate(across(all_of(allPreds), base::scale, .names = "{.col}_s")) 
saveRDS(modDat_1_s, file = "./models/scaledModelInputData.rds")

Subset the data to only include data for the ecoregion of interest based on classification from yes/no tree model (using bestLambda model)

if (ecoregion == "noTrees") {
  # select data for the ecoregion of interest
  modDat_1_s <- modDat_1_s %>%
    filter(treeProb_bestLambda_binary == 0)
} else if (ecoregion == "trees") {
  # select data for the ecoregion of interest
  modDat_1_s <- modDat_1_s %>%
    filter(treeProb_bestLambda_binary == 1)
} else if (ecoregion == "CONUS") {
  modDat_1_s <- modDat_1_s
}
# remove the rows that have no observations for the response variable of interest
modDat_1_s <- modDat_1_s[!is.na(modDat_1_s[,response]),]

# subset the data to only include these predictors, and remove any remaining NAs 
modDat_1_s <- modDat_1_s %>% 
  dplyr::select(prednames, paste0(prednames, "_s"), response, newRegion, Year, x, y, NA_L1NAME, NA_L2NAME) %>% 
  drop_na()

names(prednames) <- prednames
df_pred <- modDat_1_s[, prednames]

Visualize the response variable

hist(modDat_1_s[,response], main = paste0("Histogram of ",response),
     xlab = paste0(response))

create_summary <- function(df) {
  df %>% 
    pivot_longer(cols = everything(),
                 names_to = 'variable') %>% 
    group_by(variable) %>% 
    summarise(across(value, .fns = list(mean = ~mean(.x, na.rm = TRUE), min = ~min(.x, na.rm = TRUE), 
                                        median = ~median(.x, na.rm = TRUE), max = ~max(.x, na.rm = TRUE)))) %>% 
    mutate(across(where(is.numeric), round, 4))
}

modDat_1_s[prednames] %>% 
  create_summary() %>% 
  knitr::kable(caption = 'summaries of possible predictor variables') %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed")) 

summaries of possible predictor variables

variable	value_mean	value_min	value_median	value_max
AWHC	15.3069	0.1424	14.6567	35.2881
VPD_min_anom	-0.0143	-0.1740	-0.0163	0.1533
annWatDef_anom	-0.0491	-3.8657	-0.0506	1.0000
annWetDegDays_anom	0.0182	-1.8263	0.0118	1.0000
carbon	1.0512	0.0002	0.7658	39.5528
clay	19.1355	0.3458	18.3161	83.0975
coarse	8.2528	0.0000	4.8896	79.9649
frostFreeDays_anom	-3.2481	-77.4500	-2.4677	122.3261
isothermality	37.8068	23.3000	37.9389	56.0389
isothermality_anom	0.4218	-12.9447	0.3633	8.7003
prcp	371.8591	47.6797	354.9071	1937.0555
prcpTempCorr	0.0794	-0.8015	0.1748	0.7098
prcpTempCorr_anom	0.0093	-0.5936	0.0124	0.5251
prcp_dry	1.7463	0.0000	1.3134	39.5755
prcp_seasonality	1.0176	0.5182	0.9660	2.2319
prcp_seasonality_anom	-0.0126	-0.7465	-0.0059	0.4421
prcp_wet_anom	-0.0004	-1.4489	0.0104	0.7708
precp_dry_anom	-0.0299	-6.7500	0.0337	1.0000
t_warm_anom	-0.4458	-4.4614	-0.4420	2.6800
tmax_anom	-0.2540	-3.2458	-0.2884	1.6059
tmean	11.0050	-0.3824	9.7296	24.6330
tmin_anom	-0.4199	-4.0524	-0.3997	4.3809

Histograms of raw and scaled predictors

scaleFigDat_1 <- modDat_1_s %>% 
  dplyr::select(c(x, y, Year, prednames)) %>% 
  pivot_longer(cols = all_of(names(prednames)), 
               names_to = "predNames", 
               values_to = "predValues_unScaled")
scaleFigDat_2 <- modDat_1_s %>% 
  dplyr::select(c(x, y, Year, paste0(prednames, "_s"))) %>% 
  pivot_longer(cols = all_of(paste0(prednames,"_s"
                                    )), 
               names_to = "predNames", 
               values_to = "predValues_scaled", 
               names_sep = ) %>% 
  mutate(predNames = str_replace(predNames, pattern = "_s$", replacement = ""))

scaleFigDat_3 <- scaleFigDat_1 %>% 
  left_join(scaleFigDat_2)

ggplot(scaleFigDat_3) + 
  facet_wrap(~predNames, scales = "free") +
  geom_histogram(aes(predValues_unScaled), fill = "lightgrey", col = "darkgrey") + 
  geom_histogram(aes(predValues_scaled), fill = "lightblue", col = "blue") +
  xlab ("predictor variable values") + 
  ggtitle("Comparing the distribution of unscaled (grey) to scaled (blue) predictor variables")

modDat_1_s <- modDat_1_s %>% 
  rename_with(~paste0(.x, "_raw"), 
                any_of(names(prednames))) %>% 
  rename_with(~str_remove(.x, "_s$"), 
              any_of(paste0(names(prednames), "_s")))

Predictor variables compared to binned response variables

set.seed(12011993)
# vector of name of response variables
vars_response <- response
# longformat dataframes for making boxplots
df_sample_plots <-  modDat_1_s  %>% 
  slice_sample(n = 5e4) %>% 
   rename(response = all_of(response)) %>% 
  mutate(response = case_when(
    response <= .25 ~ ".25", 
    response > .25 & response <=.50 ~ ".50", 
    response > .50 & response <=.75 ~ ".75", 
    response >= .75  ~ "1", 
  )) %>% 
  dplyr::select(c(response, prednames)) %>% 
  tidyr::pivot_longer(cols = unname(prednames), 
               names_to = "predictor", 
               values_to = "value"
               )  
 

  ggplot(df_sample_plots, aes_string(x= "response", y = 'value')) +
  geom_boxplot() +
  facet_wrap(~predictor , scales = 'free_y') + 
  ylab("Predictor Variable Values") + 
    xlab(response)

Model Fitting

Visualize the spatial blocks and how they differ across environmental space

First, if there are observations in Louisiana, sub-sample them so they’re not so over-represented in the dataset

## make data into spatial format
modDat_1_sf <- modDat_1_s %>% 
  st_as_sf(coords = c("x", "y"), crs = st_crs("EPSG:4326"))


# download map info for visualization
data(state_boundaries_wgs84) 

cropped_states <- suppressMessages(state_boundaries_wgs84 %>%
  dplyr::filter(NAME!="Hawaii") %>%
  dplyr::filter(NAME!="Alaska") %>%
  dplyr::filter(NAME!="Puerto Rico") %>%
  dplyr::filter(NAME!="American Samoa") %>%
  dplyr::filter(NAME!="Guam") %>%
  dplyr::filter(NAME!="Commonwealth of the Northern Mariana Islands") %>%
  dplyr::filter(NAME!="United States Virgin Islands") %>%
  sf::st_sf() %>%
  sf::st_transform(sf::st_crs(modDat_1_sf))) #%>%
  #sf::st_crop(sf::st_bbox(modDat_1_sf)+c(-1,-1,1,1))
if (ecoregion %in% c("Forest", "eastForest", "forest")){
modDat_1_s$uniqueID <- 1:nrow(modDat_1_s)
modDat_1_sf$uniqueID <- 1:nrow(modDat_1_sf)

# find which observations overlap with Louisiana
obs_LA_temp <- st_intersects(modDat_1_sf, cropped_states[cropped_states$NAME == "Louisiana",], sparse = FALSE)
if (sum(obs_LA_temp) > 0) {
 obs_LA_1 <- modDat_1_sf[which(obs_LA_temp == TRUE, arr.ind = TRUE)[,1],]
# now, find only those within the oversampled area (near the coast)
dims <- c(xmin = 730439.1, xmax = 1042195.5, ymax = -1222745.2, ymin = -1390430.9)
badBox <- st_bbox(dims) %>% 
  st_as_sfc() %>% 
  st_set_crs(value = st_crs(modDat_1_sf))
  
obs_LA_temp2 <- st_intersects(obs_LA_1, badBox, sparse = FALSE)
obs_LA_2 <- obs_LA_1[which(obs_LA_temp2 == TRUE, arr.ind = TRUE)[,1],]

# subsample so there aren't so many 
# get every 7th observation
obs_LA_sampled <- obs_LA_2[seq(from = 1, to = nrow(obs_LA_2), by = 10),]
# remove observations that aren't sampled from the larger dataset
obsToRemove <- obs_LA_2[!(obs_LA_2$uniqueID %in% obs_LA_sampled$uniqueID),]

modDat_1_sf <- modDat_1_sf[!(modDat_1_sf$uniqueID %in% obsToRemove$uniqueID),]
modDat_1_s <- modDat_1_s[!(modDat_1_s$uniqueID %in% obsToRemove$uniqueID),] 
}
}

## do a pca of climate across level 2 ecoregions
pca <- prcomp(modDat_1_s[,paste0(prednames)])
library(factoextra)
(fviz_pca_ind(pca, habillage = modDat_1_s$NA_L2NAME, label = "none", addEllipses = TRUE, ellipse.level = .95, ggtheme = theme_minimal(), alpha.ind = .1))

# for ecoregions that are very tiny/extremely different from the rest of the other recoregions climatically, aggregate them together
if(ecoregion == "noTrees") {
   modDat_1_s[modDat_1_s$NA_L2NAME %in% c("EVERGLADES", "SOUTHEASTERN USA PLAINS", "TEXAS-LOUISIANA COASTAL PLAIN", "MISSISSIPPI ALLUVIAL AND SOUTHEAST USA COASTAL PLAINS", "TAMAULIPAS-TEXAS SEMIARID PLAIN"), "NA_L2NAME"] <- "SOUTHEASTERN USA PLAINS AND EVERGLADES AND LOUISIANA PLAIN"
   modDat_1_sf[modDat_1_sf$NA_L2NAME %in% c("EVERGLADES", "SOUTHEASTERN USA PLAINS", "TEXAS-LOUISIANA COASTAL PLAIN", "MISSISSIPPI ALLUVIAL AND SOUTHEAST USA COASTAL PLAINS", "TAMAULIPAS-TEXAS SEMIARID PLAIN"), "NA_L2NAME"] <- "SOUTHEASTERN USA PLAINS AND EVERGLADES AND LOUISIANA PLAIN"

}

# make a table of n for each region
modDat_1_s %>% 
  group_by(NA_L2NAME) %>% 
  dplyr::summarize("Number_Of_Observations" = length(NA_L2NAME)) %>% 
  rename("Level_2_Ecoregion" = NA_L2NAME)%>% 
  kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed")) 

Level_2_Ecoregion	Number_Of_Observations
COLD DESERTS	162248
MARINE WEST COAST FOREST	8
MEDITERRANEAN CALIFORNIA	8808
MIXED WOOD PLAINS	227
MIXED WOOD SHIELD	486
SOUTH CENTRAL SEMIARID PRAIRIES	76509
SOUTHEASTERN USA PLAINS AND EVERGLADES AND LOUISIANA PLAIN	8675
TEMPERATE PRAIRIES	8970
UPPER GILA MOUNTAINS	4006
WARM DESERTS	67633
WEST-CENTRAL SEMIARID PRAIRIES	87362
WESTERN CORDILLERA	15320
WESTERN SIERRA MADRE PIEDMONT	5542

Then, look at the spatial distribution and environmental characteristics of the grouped ecoregions

map1 <- ggplot() +
  geom_sf(data=cropped_states,fill='white') +
  geom_sf(data=modDat_1_sf#[modDat_1_sf$NA_L2NAME %in% c("MIXED WOOD PLAINS"),]
          ,
          aes(fill=as.factor(NA_L2NAME)),linewidth=0.5,alpha=0.5) +
  geom_point(data=modDat_1_s#[modDat_1_s$NA_L2NAME %in% c("MIXED WOOD PLAINS"),]
             ,
             alpha=0.5, 
             aes(x = x, y = y, color=as.factor(NA_L2NAME)), alpha = .1) +
  #scale_fill_okabeito() +
  #scale_color_okabeito() +
 # theme_default() +
  theme(legend.position = 'none') +
  labs(title = "Level 2 Ecoregions as spatial blocks")

hull <- modDat_1_sf %>%
  ungroup() %>%
  group_by(NA_L2NAME) %>%
  slice(chull(tmean, prcp))

plot1<-ggplot(data=modDat_1_sf,aes(x=tmean,y=prcp)) +
  geom_polygon(data = hull, alpha = 0.25,aes(fill=NA_L2NAME) )+
  geom_point(aes(group=NA_L2NAME,color=NA_L2NAME),alpha=0.25) +
  theme_minimal() + xlab("Annual Average T_mean - long-term average") +
  ylab("Annual Average Precip - long-term average") #+
  #scale_color_okabeito() +
  #scale_fill_okabeito()

plot2<-ggplot(data=modDat_1_sf %>%
                pivot_longer(cols=tmean:prcp),
              aes(x=value,group=name)) +
  # geom_polygon(data = hull, alpha = 0.25,aes(fill=fold) )+
  geom_density(aes(group=NA_L2NAME,fill=NA_L2NAME),alpha=0.25) +
  theme_minimal() +
  facet_wrap(~name,scales='free')# +
  #scale_color_okabeito() +
  #scale_fill_okabeito()
 
library(patchwork)
(combo <- (map1+plot1)/plot2) 

# 
# ggplot(data = modDat_1_s) +
#   geom_density(aes(ShrubCover_transformed, col = NA_L2NAME)) +
#   xlim(c(0,100))

Fit a global model with all of the data

First, fit a LASSO regression model using the glmnet R package

• This regression is a beta glm with a logit link (using custom function from Daniel)
• Use cross validation across level 2 ecoregions to tune the lambda parameter in the LASSO model
• this model is fit to using the scaled weather/climate/soils variables
• this list of possible predictors includes:
  1. main effects
  2. interactions between all soils variables
  3. interactions between climate and weather variables
  4. transformed main effects (squared, log-transformed (add a uniform integer – 20– to all variables prior to log-transformation), square root-transformed (add a uniform integer – 20– to all variables prior to log-transformation))

Get rid of transformed predictions and interactions that are correlated

# get first pass of names correlated variables
X_df <- X %>% 
  as.data.frame() %>% 
  dplyr::select(-'(Intercept)')  
corrNames_i <- X_df %>% 
  cor()  %>% 
   caret::findCorrelation(cutoff = .7, verbose = FALSE, names = TRUE, exact = TRUE)
# remove those names that are untransformed main effects 
  # vector of columns to remove 
badNames <- corrNames_i[!(corrNames_i %in% prednames)]
while (sum(!(corrNames_i %in% prednames))>0) {
 corrNames_i <-  X_df %>% 
    dplyr::select(-badNames) %>% 
     cor()  %>% 
   caret::findCorrelation(cutoff = .7, verbose = FALSE, names = TRUE, exact = TRUE)
 # update the vector of names to remove 
 badNames <- unique(c(badNames, corrNames_i[!(corrNames_i %in% prednames)]))
}

## see if there are any correlated variables left (would be all main effects at this point)
# if there are, step through and remove the variable that each is most correlated with 
if (length(corrNames_i)>1) {
  for (i in 1:length(corrNames_i)) {
    X_i <- X_df %>% 
      dplyr::select(-badNames)
    if (corrNames_i[i] %in% names(X_i)) {
    corMat_i <- cor(x = X_i[corrNames_i[i]], y = X_i %>% dplyr::select(-corrNames_i[i])) 
    badNames_i <- colnames(corMat_i)[abs(corMat_i)>=.7]
    # if there are any predictors in the 'badNames_i', remove them from this list
    if (length(badNames_i) > 0 & sum(c(badNames_i %in% prednames))>0) {
        badNames_i <- badNames_i[!(badNames_i %in% prednames)]
    }
    badNames <- unique(c(badNames, badNames_i))
    }
  }
}
## update the X matrix to exclude these correlated variables
X <- X[,!(colnames(X) %in% badNames)]

if (run == TRUE) {
  # set up custom folds
    # get the ecoregions for training lambda
  train_eco <- modDat_1_s$NA_L2NAME#[train]
  
  # Fit model -----------------------------------------------
  # specify leave-one-year-out cross-validation
  my_folds <- as.numeric(as.factor(train_eco))

    # set up parallel processing
    library(doMC)
    # this computer has 16 cores (parallel::detectCores())
    registerDoMC(cores = 8)
    
    fit <- cv.glmnet(
      x = X[,2:ncol(X)], 
      y = y, 
      family = quasibeta_family(),
      keep = FALSE,
      alpha = 1,  # 0 == ridge regression, 1 == lasso, 0.5 ~~ elastic net
      lambda = lambdas,
      relax = ifelse(response == "ShrubCover", yes = TRUE, no = FALSE),
      #nlambda = 100,
      type.measure="mse",
      #penalty.factor = pen_facts,
      foldid = my_folds,
      #thresh = thresh,
      standardize = FALSE, ## scales variables prior to the model sequence... coefficients are always returned on the original scale
      parallel = TRUE
    )
     base::saveRDS(fit, paste0("../ModelFitting/models/betaLASSO/", response, "_globalLASSOmod_betaLogitLink_",ecoregion,"_removeAnomalies", removeAllAnoms,".rds"))
    
    
     best_lambda <- fit$lambda.min
  # save the lambda for the most regularized model w/ an MSE that is still 1SE w/in the best lambda model
  lambda_1SE <- fit$lambda.1se
  # save the lambda for the most regularized model w/ an MSE that is still .5SE w/in the best lambda model
  lambda_halfSE <- best_lambda + ((lambda_1SE - best_lambda)/2)
 
## Now, we need to do stability selection to ensure the coefficients that are being chosen with each lambda are stable 

## stability selection for best lambda model 
# setup params
p <- ncol(X[,2:ncol(X)]) # of parameters
n <- length(y) # of observations
n_iter <- 100        # number of subsamples
sample_frac <- 0.75  # fraction of data to subsample
lambda_val <- best_lambda    # fixed lambda value (could be chosen via CV)

# Track selection
selection_counts_bestL <- matrix(0, nrow = p, ncol = 1)

for (i in 1:n_iter) {
  # Subsample rows
  sample_idx <- sample(1:n, size = floor(sample_frac * n), replace = FALSE)
  X_sub <- X[sample_idx, ]
  y_sub <- y[sample_idx]

  # Fit Lasso model
  fit_stab_i <- glmnet(x = X_sub[,2:ncol(X_sub)], y = y_sub, 
    family = quasibeta_family(),
    alpha = 1, lambda = lambda_val, standardize = FALSE)

  # Get non-zero coefficients (excluding intercept)
  select_bestL <- which(as.vector(coef(fit_stab_i))[-1] != 0)
  selection_counts_bestL[select_bestL] <- selection_counts_bestL[select_bestL] + 1
}

# Convert counts to selection probabilities (the probability that a variable is selected over 100 iterations)
selection_prob_bestL <- selection_counts_bestL / n_iter
selection_prob_bestL_df <- data.frame(
  VariableNumber = paste0("X", 1:p),
  VariableName = rownames(coef(fit_stab_i))[2:(p+1)],
  SelectionProb = as.vector(selection_prob_bestL)
)

# get those variables that are selected in ≥70% of subsets (Meinshausen and Bühlmann, 2010)
bestLambda_coef <- selection_prob_bestL_df[selection_prob_bestL_df$SelectionProb>=.7, c("VariableName", "SelectionProb")]

#//////
# stability selection for 1se lambda model
lambda_val <-  lambda_1SE    # fixed lambda value (could be chosen via CV)

# Track selection
selection_counts_1seL <- matrix(0, nrow = p, ncol = 1)

for (i in 1:n_iter) {
  # Subsample rows
  sample_idx <- sample(1:n, size = floor(sample_frac * n), replace = FALSE)
  X_sub <- X[sample_idx, ]
  y_sub <- y[sample_idx]

  # Fit Lasso model
  fit_stab_i <- glmnet(x = X_sub[,2:ncol(X_sub)], y = y_sub, 
    family = quasibeta_family(),
    alpha = 1, lambda = lambda_val, standardize = FALSE)

  # Get non-zero coefficients (excluding intercept)
  selected_1seL <- which(as.vector(coef(fit_stab_i))[-1] != 0)
  selection_counts_1seL[selected_1seL] <- selection_counts_1seL[selected_1seL] + 1
}

# Convert counts to selection probabilities (the probability that a variable is selected over 100 iterations)
selection_prob_1seL <- selection_counts_1seL / n_iter
selection_prob_1seL_df <- data.frame(
  VariableNumber = paste0("X", 1:p),
  VariableName = rownames(coef(fit_stab_i))[2:(p+1)],
  SelectionProb = as.vector(selection_prob_1seL)
)

# get those variables that are selected in ≥70% of subsets (Meinshausen and Bühlmann, 2010)
seLambda_coef <- selection_prob_1seL_df[selection_prob_1seL_df$SelectionProb>=.7, c("VariableName", "SelectionProb")]

# stability selection for half se lambda model
lambda_val <- lambda_halfSE    # fixed lambda value (could be chosen via CV)

# Track selection
selection_counts_halfseL <- matrix(0, nrow = p, ncol = 1)

for (i in 1:n_iter) {
  # Subsample rows
  sample_idx <- sample(1:n, size = floor(sample_frac * n), replace = FALSE)
  X_sub <- X[sample_idx, ]
  y_sub <- y[sample_idx]

  # Fit Lasso model
  fit_stab_i <- glmnet(x = X_sub[,2:ncol(X_sub)], y = y_sub, 
    family = quasibeta_family(),
    alpha = 1, lambda = lambda_val, standardize = FALSE)

  # Get non-zero coefficients (excluding intercept)
  selected_halfseL <- which(as.vector(coef(fit_stab_i))[-1] != 0)
  selection_counts_halfseL[selected_halfseL] <- selection_counts_halfseL[selected_halfseL] + 1
}

# Convert counts to selection probabilities (the probability that a variable is selected_halfseL over 100 iterations)
selection_prob_halfseL <- selection_counts_halfseL / n_iter
selection_prob_halfseL_df <- data.frame(
  VariableNumber = paste0("X", 1:p),
  VariableName = rownames(coef(fit_stab_i))[2:(p+1)],
  SelectionProb = as.vector(selection_prob_halfseL)
)

# get those variables that are selected_halfseL_halfseL in ≥70% of subsets (Meinshausen and Bühlmann, 2010)
halfseLambda_coef <- selection_prob_halfseL_df[selection_prob_halfseL_df$SelectionProb>=.7, c("VariableName", "SelectionProb")]

## If prompted to do so by the input arguments, remove any predictors that are for weather anomalies whose corresponding climate predictor is not included in the model 
if (trimAnom == TRUE) {
  # get unique predictors
  bestLamb_all <- bestLambda_coef$VariableName %>% #[str_detect(bestLambda_coef$VariableName, pattern = "_anom_s")] %>% 
    str_remove(pattern = "I\\(") %>% 
    str_remove(pattern = "\\^2\\)") %>% 
    str_remove(pattern = "\\^2\\)") %>% 
    str_split(pattern = ":", simplify = TRUE) 
  if (ncol(bestLamb_all) == 1) {
    bestLamb_all <- unique(bestLamb_all)
  } else {
    bestLamb_all <-  c(bestLamb_all[bestLamb_all[,1] !="",1], bestLamb_all[bestLamb_all[,2] !="",2]) %>% 
      unique()
  }
  # get anomalies
   bestLamb_anom <- bestLamb_all[bestLamb_all %in% prednames_weath]
  # get climate
   bestLamb_clim <- bestLamb_all[bestLamb_all %in% prednames_clim]
  # which anomalies are present in the predictors, but their corresponding climate variable isn't
   bestLamb_anomsWithMissingClim <- bestLamb_anom[!(str_remove(bestLamb_anom, "_anom") %in% bestLamb_clim)]
   # remove anomalies (and all interaction terms w/ those anomalies) from the predictor list

   if (length(bestLamb_anomsWithMissingClim) != 0) {
   
        bestLambda_coef_NEW <- bestLambda_coef
      for (i in 1:length(bestLamb_anomsWithMissingClim)) {
     bestLambda_coef_NEW <- bestLambda_coef_NEW[!str_detect(bestLambda_coef_NEW$VariableName, pattern = bestLamb_anomsWithMissingClim[i]),]
      }
     
   bestLambda_coef <- bestLambda_coef_NEW
   }
   
   
  #//// 1 se lambda model
      if (nrow(seLambda_coef) !=0) {
        # get unique predictors
  seLamb_all <- seLambda_coef$VariableName %>% #[str_detect(seLambda_coef$VariableName, pattern = "_anom_s")] %>% 
    str_remove(pattern = "I\\(") %>% 
    str_remove(pattern = "_s\\^2\\)") %>% 
    str_remove(pattern = "\\^2\\)") %>% 
    str_split(pattern = ":", simplify = TRUE) 
  if (ncol(seLamb_all) == 1) {
    seLamb_all <- unique(seLamb_all)
  } else {
    seLamb_all <-  c(seLamb_all[seLamb_all[,1] !="",1], seLamb_all[seLamb_all[,2] !="",2]) %>% 
      unique()
  }
  # get anomalies
   seLamb_anom <- seLamb_all[seLamb_all %in% prednames_weath]
  # get climate
   seLamb_clim <- seLamb_all[seLamb_all %in% prednames_clim]
  # which anomalies are present in the predictors, but their corresponding climate variable isn't
   seLamb_anomsWithMissingClim <- seLamb_anom[!(str_remove(seLamb_anom, "_anom") %in%  seLamb_clim)]
   # remove anomalies (and all interaction terms w/ those anomalies) from the predictor list
      if (length(seLamb_anomsWithMissingClim) != 0) {
    seLambda_coef_NEW <- seLambda_coef
   for (i in 1:length(seLamb_anomsWithMissingClim)) {
     seLambda_coef_NEW <- seLambda_coef_NEW[!str_detect(seLambda_coef_NEW$VariableName, pattern = seLamb_anomsWithMissingClim[i]),]
   }
   seLambda_coef <- seLambda_coef_NEW
      }
   }
  
  #//// 1 se lambda model
      if (nrow(halfseLambda_coef) !=0) {
        # get unique predictors
  halfseLamball<- halfseLambda_coef$VariableName %>% #[str_detect(halfseLambda_coef$VariableName, pattern = "_anom_s")] %>% 
    str_remove(pattern = "I\\(") %>% 
    str_remove(pattern = "_s\\^2\\)") %>% 
    str_remove(pattern = "\\^2\\)") %>% 
    str_split(pattern = ":", simplify = TRUE) 
  
    if (ncol(halfseLamball) == 1) {
    halfseLamball <- unique(halfseLamball)
  } else {
    halfseLamball <-  c(halfseLamball[halfseLamball[,1] !="",1], halfseLamball[halfseLamball[,2] !="",2]) %>% 
      unique()
  }
  
  # get anomalies
   halfseLambanom <- halfseLamball[halfseLamball %in% prednames_weath]
  # get climate
   halfseLambclim <- halfseLamball[halfseLamball %in% prednames_clim]
  # which anomalies are present in the predictors, but their corresponding climate variable isn't
   halfseLambanomsWithMissingClim <- halfseLambanom[!(str_remove(halfseLambanom, "_anom_s") %in%  halfseLambclim)]
   # remove anomalies (and all interaction terms w/ those anomalies) from the predictor list

   
   ##
        if (length(halfseLambanomsWithMissingClim) != 0) {
   halfseLambda_coef_NEW <- halfseLambda_coef
   for (i in 1:length(halfseLambanomsWithMissingClim)) {
     halfseLambda_coef_NEW <- halfseLambda_coef_NEW[!str_detect(halfseLambda_coef_NEW$VariableName, pattern = halfseLambanomsWithMissingClim[i]),]
   }
   halfseLambda_coef <- halfseLambda_coef_NEW
      }
   }
    ##
  
      }


## 
## fit w/ the identified coefficients from the 'best' lambda, but using the glm function
  mat_glmnet_best <- bestLambda_coef$VariableName 

  if (length(mat_glmnet_best) == 0) {
    f_glm_bestLambda <- as.formula(paste0(response, "~ 1"))
  } else {
  f_glm_bestLambda <- as.formula(paste0(response, " ~ ", paste0(mat_glmnet_best, collapse = " + ")))
  }
  
## fit using betareg
  fit_glm_bestLambda <- fit_glm_bestLambda_quasiBETA <- glm(formula = f_glm_bestLambda, data = modDat_1_s, family =quasibeta_family(link = "logit") )
    
  #fit_glm_bestLambda_BETAREG <- betareg(formula =  f_glm_bestLambda, data = modDat_1_s, link = "logit")
  ## fit using quasi-beta
  # ## compare coefficients
  # modCoeffsTest <- data.frame("coefficientName" = names(coefficients(fit_glm_bestLambda_BETAREG)),
  #                             "coefficientValue" = coefficients(fit_glm_bestLambda_BETAREG), 
  #                             "confint_low" = confint(fit_glm_bestLambda_BETAREG)[,1],
  #                             "confint_high" = confint(fit_glm_bestLambda_BETAREG)[,2],
  #                             "type" = "betareg") %>% 
  #   rbind(data.frame("coefficientName" = names(coefficients(fit_glm_bestLambda_quasiBETA)),
  #                             "coefficientValue" = coefficients(fit_glm_bestLambda_quasiBETA), 
  #                             "confint_low" = coefficients(fit_glm_bestLambda_quasiBETA) - ( summary(fit_glm_bestLambda_quasiBETA)$coefficients[,2] * 1.96) ,
  #                             "confint_high" = coefficients(fit_glm_bestLambda_quasiBETA) + ( summary(fit_glm_bestLambda_quasiBETA)$coefficients[,2] * 1.96),
  #                             "type" = "quasiBeta")) %>% 
  #   filter(coefficientName != "(phi)")
  # ggplot(data = modCoeffsTest) + 
  #   geom_point(aes(x = coefficientValue, y = coefficientName, col = type)) + 
  #   geom_errorbar(aes(xmin = confint_low, xmax = confint_high, y = coefficientName, col = type)) + 
  #   geom_vline(aes(xintercept = 0), lty = 3)
  # 
   ## fit w/ the identified coefficients from the '1se' lambda, but using the glm function
  mat_glmnet_1se <- seLambda_coef$VariableName
    
  if (length(mat_glmnet_1se) == 0) {
    f_glm_1se <- as.formula(paste0(response, "~ 1"))
  } else {
  f_glm_1se <- as.formula(paste0(response, " ~ ", paste0(mat_glmnet_1se, collapse = " + ")))
  }


  fit_glm_se <- glm(formula = f_glm_1se, data = modDat_1_s, family =quasibeta_family(link = "logit") )
  # glm(data = modDat_1_s, formula = f_glm_1se,
  #                   family =  stats::Gamma(link = "log"))
  
     ## fit w/ the identified coefficients from the '.5se' lambda, but using the glm function
  mat_glmnet_halfse <- halfseLambda_coef$VariableName
  
  if (length(mat_glmnet_halfse) == 0) {
    f_glm_halfse <- as.formula(paste0(response, "~ 1"))
  } else {
  f_glm_halfse <- as.formula(paste0(response, " ~ ", paste0(mat_glmnet_halfse, collapse = " + ")))
  }

  fit_glm_halfse <- glm(formula = f_glm_halfse, data = modDat_1_s, family =quasibeta_family(link = "logit") )
  
  ## save models 
  if (trimAnom == TRUE) {
    saveRDS(fit_glm_bestLambda, paste0("./models/betaLASSO/",response,"_",ecoregion, "_noTLP_",removeTLP,"_removeAnomalies", removeAllAnoms,"_trimAnom_bestLambdaGLM.rds"))
  saveRDS(fit_glm_halfse, paste0("./models/betaLASSO/",response,"_",ecoregion, "_noTLP_",removeTLP,"_removeAnomalies", removeAllAnoms,"_trimAnom_halfSELambdaGLM.rds"))
  saveRDS(fit_glm_se, paste0("./models/betaLASSO/",response,"_",ecoregion, "_noTLP_",removeTLP,"_removeAnomalies", removeAllAnoms,"_trimAnom_oneSELambdaGLM.rds"))
  } else {
    saveRDS(fit_glm_bestLambda, paste0("./models/betaLASSO/",response,"_",ecoregion, "_noTLP_",removeTLP,"_removeAnomalies", removeAllAnoms,"_bestLambdaGLM.rds"))
  saveRDS(fit_glm_halfse, paste0("./models/betaLASSO/",response,"_",ecoregion, "_noTLP_",removeTLP,"_removeAnomalies", removeAllAnoms,"_halfSELambdaGLM.rds"))
  saveRDS(fit_glm_se, paste0("./models/betaLASSO/",response,"_",ecoregion, "_noTLP_",removeTLP,"_removeAnomalies", removeAllAnoms,"_oneSELambdaGLM.rds"))
    
  }
  
  ## save the R environment after running the models 
  save(f_glm_halfse, mat_glmnet_halfse, halfseLambda_coef,
              f_glm_1se, mat_glmnet_1se, seLambda_coef,
              f_glm_bestLambda, mat_glmnet_best, bestLambda_coef,
              file = paste0("./models/interimModelFittingObjects_", response, "_", ecoregion, "_removeAnomalies", removeAllAnoms,"_betaReg.rds" ))
  } else {
    # read in LASSO object
    fit <- readRDS(paste0("../ModelFitting/models/betaLASSO/", response, "_globalLASSOmod_betaLogitLink_",ecoregion,"_removeAnomalies", removeAllAnoms,".rds"))
    
    # read in R objects having to do w/ model fitting 
    load(file = paste0("./models/interimModelFittingObjects_", response, "_", ecoregion, "_removeAnomalies", removeAllAnoms,"_betaReg.rds" ))
      
    if (trimAnom == TRUE) {
    fit_glm_bestLambda <- readRDS( paste0("./models/betaLASSO/",response,"_",ecoregion, "_noTLP_",removeTLP,"_removeAnomalies", removeAllAnoms,"_trimAnom_bestLambdaGLM.rds"))
  fit_glm_halfse <- readRDS( paste0("./models/betaLASSO/",response,"_",ecoregion, "_noTLP_",removeTLP,"_removeAnomalies", removeAllAnoms,"_trimAnom_halfSELambdaGLM.rds"))
 fit_glm_se <- readRDS( paste0("./models/betaLASSO/",response,"_",ecoregion, "_noTLP_",removeTLP,"_removeAnomalies", removeAllAnoms,"_trimAnom_oneSELambdaGLM.rds"))
  } else {
    fit_glm_bestLambda <- readRDS( paste0("./models/betaLASSO/",response,"_",ecoregion, "_noTLP_",removeTLP,"_removeAnomalies", removeAllAnoms,"_bestLambdaGLM.rds"))
  fit_glm_halfse <- readRDS( paste0("./models/betaLASSO/",response,"_",ecoregion, "_noTLP_",removeTLP,"_removeAnomalies", removeAllAnoms,"_halfSELambdaGLM.rds"))
  fit_glm_se <- readRDS( paste0("./models/betaLASSO/",response,"_",ecoregion, "_noTLP_",removeTLP,"_removeAnomalies", removeAllAnoms,"_oneSELambdaGLM.rds"))
    
  }
    
  }


  # assess model fit
  # assess.glmnet(fit$fit.preval, #newx = X[,2:293], 
  #               newy = y, family = stats::Gamma(link = "log"))
  # save the minimum lambda
  best_lambda <- fit$lambda.min
  # save the lambda for the most regularized model w/ an MSE that is still 1SE w/in the best lambda model
  lambda_1SE <- fit$lambda.1se
  # save the lambda for the most regularized model w/ an MSE that is still .5SE w/in the best lambda model
  lambda_halfSE <- best_lambda + ((lambda_1SE - best_lambda)/2)
 
  print(fit)     

## 
## Call:  cv.glmnet(x = X[, 2:ncol(X)], y = y, lambda = lambdas, type.measure = "mse",      foldid = my_folds, keep = FALSE, parallel = TRUE, relax = ifelse(response ==          "ShrubCover", yes = TRUE, no = FALSE), family = quasibeta_family(),      alpha = 1, standardize = FALSE) 
## 
## Measure: Mean-Squared Error 
## 
##       Lambda Index Measure       SE Nonzero
## min 0.000010   200 0.03205 0.003555     170
## 1se 0.001589   127 0.03552 0.004731      83

  plot(fit)

Then, we predict (on the training set) using both of these models (best lambda and 1se lambda)

  ## predict on the test data
  # lasso model predictions with the optimal lambda
  optimal_pred <- predict(fit_glm_bestLambda, newx=X[,2:ncol(X)], type = "response")
  optimal_pred_1se <-  predict(fit_glm_se, newx=X[,2:ncol(X)], type = "response")
  optimal_pred_halfse <- predict(fit_glm_halfse, newx = X[,2:ncol(X)], type = "response")
  
    null_fit <- glm(#data = data.frame("y" = y, X[,paste0(prednames, "_s")]), 
      formula = y ~ 1, #data = modDat_1_s, 
      family = quasibeta_family(link = "logit")
      #formula = y ~ 1, family = stats::Gamma(link = "log")
      )
  null_pred <- predict(null_fit, newdata = as.data.frame(X), type = "response"
                       )

  # ## snap values above 100 and below 0 to be 100 or z
  # #optimal_pred[optimal_pred>100] <- 100
  # optimal_pred[optimal_pred<0] <- 0
  # #optimal_pred_1se[optimal_pred_1se>100] <- 100
  # optimal_pred_1se[optimal_pred_1se<0] <- 0
  # #optimal_pred_halfse[optimal_pred_halfse>100] <- 100
  # optimal_pred_halfse[optimal_pred_halfse<0] <- 0
  # 
  # save data
  fullModOut <- list(
    "modelObject" = fit,
    "nullModelObject" = null_fit,
    "modelPredictions" = data.frame(#ecoRegion_holdout = rep(test_eco,length(y)),
      obs=y,
                    pred_opt=optimal_pred, 
                    pred_opt_se = optimal_pred_1se,
                    pred_opt_halfse = optimal_pred_halfse,
                    pred_null=null_pred#,
                    #pred_nopenalty=nopen_pred
                    ))

ggplot() + 
  geom_point(aes(X[,2], fullModOut$modelPredictions$obs), col = "black", alpha = .1) + 
  geom_point(aes(X[,2], fullModOut$modelPredictions$pred_opt), col = "red", alpha = .1) + ## predictions w/ the CV model
  geom_point(aes(X[,2], fullModOut$modelPredictions$pred_opt_halfse), col = "orange", alpha = .1) + ## predictions w/ the CV model (.5se lambda)
  geom_point(aes(X[,2], fullModOut$modelPredictions$pred_opt_se), col = "green", alpha = .1) + ## predictions w/ the CV model (1se lambda)
  geom_point(aes(X[,2], fullModOut$modelPredictions$pred_null), col = "blue", alpha = .1) + 
  labs(title = "A rough comparison of observed and model-predicted values", 
       subtitle = "black = observed values \n red = predictions from 'best lambda' model \n orange = predictions for '1/2se' lambda model \n green = predictions from '1se' lambda model \n blue = predictions from null model") +
  xlab(colnames(X)[2])

  #ylim(c(0,200))

The internal cross-validation process to fit the global LASSO model identified an optimal lambda value (regularization parameter) of r{print(best_lambda)}. The lambda value such that the cross validation error is within 1 standard error of the minimum (“1se lambda”) was `r{print(fit$lambda.1se)}`` . The following coefficients were kept in each model:

# the coefficient matrix from the 'best model' -- find and print those coefficients that aren't 0 in a table
# the coefficient matrix from the 'best model' -- find and print those coefficients that aren't 0 in a table
coef_glm_bestLambda <- coef(fit_glm_bestLambda) %>% 
  data.frame() 
coef_glm_bestLambda$coefficientName <- rownames(coef_glm_bestLambda)
names(coef_glm_bestLambda)[1] <- "coefficientValue_bestLambda"
# coefficient matrix from the '1se' model 
coef_glm_1se <- coef(fit_glm_se) %>% 
  data.frame() 
coef_glm_1se$coefficientName <- rownames(coef_glm_1se)
names(coef_glm_1se)[1] <- "coefficientValue_1seLambda"
# coefficient matrix from the 'half se' model 
coef_glm_halfse <- coef(fit_glm_halfse) %>% 
  data.frame() 
coef_glm_halfse$coefficientName <- rownames(coef_glm_halfse)
names(coef_glm_halfse)[1] <- "coefficientValue_halfseLambda"
# add together
coefs <- full_join(coef_glm_bestLambda, coef_glm_halfse) %>% 
  full_join(coef_glm_1se) %>% 
  dplyr::select(coefficientName, coefficientValue_bestLambda,
                coefficientValue_halfseLambda, coefficientValue_1seLambda)

globModTerms <- coefs[!is.na(coefs$coefficientValue_bestLambda), "coefficientName"]

## also, get the number of unique variables in each model 
var_prop_pred <- paste0(response, "_pred")
response_vars <- c(response, var_prop_pred)
# for best lambda model
prednames_fig <- paste(str_split(globModTerms, ":", simplify = TRUE)) 
prednames_fig <- str_replace(prednames_fig, "I\\(", "")
prednames_fig <- str_replace(prednames_fig, "\\^2\\)", "")
prednames_fig <- unique(prednames_fig[prednames_fig>0])
prednames_fig <- prednames_fig
prednames_fig_num <- length(prednames_fig)
# for 1SE lambda model
globModTerms_1se <- coefs[!is.na(coefs$coefficientValue_1seLambda), "coefficientName"]
if (length(globModTerms_1se) == 1) {
prednames_fig_1se <- paste(str_split(globModTerms_1se, ":", simplify = TRUE)) 
prednames_fig_1se <- str_replace(prednames_fig_1se, "I\\(", "")
prednames_fig_1se <- str_replace(prednames_fig_1se, "\\^2\\)", "")
prednames_fig_1se <- unique(prednames_fig_1se[prednames_fig_1se>0])
prednames_fig_1se_num <- c(0)
} else {
prednames_fig_1se <- paste(str_split(globModTerms_1se, ":", simplify = TRUE)) 
prednames_fig_1se <- str_replace(prednames_fig_1se, "I\\(", "")
prednames_fig_1se <- str_replace(prednames_fig_1se, "\\^2\\)", "")
prednames_fig_1se <- unique(prednames_fig_1se[prednames_fig_1se>0])
prednames_fig_1se_num <- length(prednames_fig_1se)
}
# for 1/2SE lambda model
globModTerms_halfse <- coefs[!is.na(coefs$coefficientValue_halfseLambda), "coefficientName"]
if (length(globModTerms_halfse) == 1) {
prednames_fig_halfse <- paste(str_split(globModTerms_halfse, ":", simplify = TRUE)) 
prednames_fig_halfse <- str_replace(prednames_fig_halfse, "I\\(", "")
prednames_fig_halfse <- str_replace(prednames_fig_halfse, "\\^2\\)", "")
prednames_fig_halfse <- unique(prednames_fig_halfse[prednames_fig_halfse>0])
prednames_fig_halfse_num <- c(0)
} else {
prednames_fig_halfse <- paste(str_split(globModTerms_halfse, ":", simplify = TRUE)) 
prednames_fig_halfse <- str_replace(prednames_fig_halfse, "I\\(", "")
prednames_fig_halfse <- str_replace(prednames_fig_halfse, "\\^2\\)", "")
prednames_fig_halfse <- unique(prednames_fig_halfse[prednames_fig_halfse>0])
prednames_fig_halfse_num <- length(prednames_fig_halfse)
}
# make a table
kable(coefs, col.names = c("Coefficient Name", "Value from best lambda model", 
                           "Value from 1/2 se lambda", "Value from 1se lambda model")
      ) %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed")) 

Coefficient Name	Value from best lambda model	Value from 1/2 se lambda	Value from 1se lambda model
(Intercept)	-0.1671143	-0.4732627	-0.3629785
tmean	-0.0950084	-0.0369307	NA
prcp	0.7980853	0.8341862	0.8668923
prcp_dry	0.6586892	0.1215206	NA
prcp_seasonality	0.3656117	NA	NA
prcpTempCorr	0.2606384	0.3553900	0.3345602
isothermality	-0.0160497	-0.0353492	-0.0565954
clay	0.1719575	0.1894285	0.1738729
coarse	-0.1674358	-0.1568491	-0.1324571
carbon	0.0406166	NA	NA
AWHC	0.0098447	0.0106689	0.0134756
prcp_seasonality_anom	0.0185440	NA	0.0130258
prcpTempCorr_anom	0.0140155	NA	NA
isothermality_anom	-0.0330117	NA	NA
I(tmean^2)	-0.1520347	-0.1267613	-0.1463930
I(prcp_dry^2)	0.1968296	NA	NA
I(prcpTempCorr^2)	0.4694900	0.5230361	0.4724808
I(isothermality^2)	-0.1187736	-0.1121530	-0.1382563
I(prcp_seasonality_anom^2)	-0.0142580	NA	-0.0121400
I(prcpTempCorr_anom^2)	-0.0384174	NA	-0.0395436
I(isothermality_anom^2)	-0.0008091	NA	NA
I(clay^2)	0.0039681	0.0048565	0.0009240
I(coarse^2)	0.0401033	0.0434446	0.0333825
I(AWHC^2)	-0.1347503	-0.1361126	-0.1395202
isothermality:isothermality_anom	0.0147836	NA	NA
prcp_dry:isothermality	0.8514898	0.8151718	NA
prcp_seasonality:isothermality	0.2925600	NA	NA
isothermality:prcp_seasonality_anom	-0.0366580	NA	-0.0248229
prcpTempCorr:isothermality	0.0604200	0.0633384	NA
isothermality:prcpTempCorr_anom	-0.0117492	NA	NA
prcp:isothermality_anom	-0.0501168	NA	NA
prcp_seasonality:isothermality_anom	-0.0111170	NA	-0.0145218
prcp_seasonality_anom:isothermality_anom	0.0147447	NA	NA
prcpTempCorr:isothermality_anom	-0.0166868	NA	-0.0163055
prcpTempCorr_anom:isothermality_anom	0.0018008	NA	NA
tmean:isothermality_anom	-0.0205748	NA	NA
prcp:prcp_seasonality_anom	-0.0856850	NA	-0.0869796
prcp_dry:prcp_seasonality	0.7259404	NA	NA
prcp_dry:prcpTempCorr	-0.1789411	-0.0920083	NA
prcp_dry:prcpTempCorr_anom	0.0573809	NA	NA
tmean:prcp_dry	-0.3987732	-0.1806888	NA
prcp_seasonality:prcp_seasonality_anom	-0.0192139	NA	NA
prcp_seasonality:prcpTempCorr	0.1266454	NA	NA
prcpTempCorr:prcp_seasonality_anom	0.0123088	NA	0.0090124
prcp_seasonality_anom:prcpTempCorr_anom	-0.0110988	NA	-0.0069117
tmean:prcp_seasonality_anom	0.0332842	NA	NA
prcpTempCorr:prcpTempCorr_anom	-0.0165332	NA	-0.0112075
tmean:prcpTempCorr	-0.2886147	-0.2930025	NA
tmean:prcpTempCorr_anom	0.0065871	NA	NA
carbon:AWHC	-0.2162889	NA	NA
clay:AWHC	-0.0851975	-0.0971970	-0.0990364
coarse:AWHC	-0.0477575	-0.0446505	-0.0481569
coarse:carbon	-0.2216989	-0.1931301	-0.1686900
clay:coarse	0.1409509	0.1470788	0.1355707
isothermality:prcp_seasonality	NA	0.2640831	0.2586032
prcpTempCorr:prcp_seasonality	NA	0.1493609	0.1682512
AWHC:carbon	NA	-0.1942555	-0.1728192
isothermality:prcp_dry	NA	NA	0.7258454
prcpTempCorr:prcp_dry	NA	NA	-0.1451350
prcp_dry:tmean	NA	NA	-0.1615620
prcpTempCorr:tmean	NA	NA	-0.2888375

# calculate RMSE of all models 
RMSE_best <- yardstick::rmse(fullModOut$modelPredictions[,c("obs", "pred_opt")], truth = "obs", estimate = "pred_opt")$.estimate
RMSE_halfse <- yardstick::rmse(fullModOut$modelPredictions[,c("obs", "pred_opt_halfse")], truth = "obs", estimate = "pred_opt_halfse")$.estimate
RMSE_1se <- yardstick::rmse(fullModOut$modelPredictions[,c("obs", "pred_opt_se")], truth = "obs", estimate = "pred_opt_se")$.estimate
# calculate bias of all models
bias_best <-  mean((fullModOut$modelPredictions$obs) - fullModOut$modelPredictions$pred_opt)
bias_halfse <-  mean((fullModOut$modelPredictions$obs) - fullModOut$modelPredictions$pred_opt_halfse)
bias_1se <- mean((fullModOut$modelPredictions$obs) - fullModOut$modelPredictions$pred_opt_se)


uniqueCoeffs <- data.frame("Best lambda model" = c(signif(RMSE_best,3), as.character(signif(bias_best, 3)),
  as.integer(length(globModTerms)-1), as.integer(prednames_fig_num), 
                                                   as.integer(sum(prednames_fig %in% c(prednames_clim))),
                                                   as.integer(sum(prednames_fig %in% c(prednames_weath))),
                                                   as.integer(sum(prednames_fig %in% c(prednames_soils)))
                                                   ), 
                           "1/2 se lambda model" = c(signif(RMSE_halfse,3), as.character(signif(bias_halfse, 3)),
                             length(globModTerms_halfse)-1, prednames_fig_halfse_num,
                                                   sum(prednames_fig_halfse %in% c(prednames_clim)),
                                                   sum(prednames_fig_halfse %in% c(prednames_weath)),
                                                   sum(prednames_fig_halfse %in% c(prednames_soils))), 
                           "1se lambda model" = c(signif(RMSE_1se,3), as.character(signif(bias_1se, 3)),
                             length(globModTerms_1se)-1, prednames_fig_1se_num,
                                                   sum(prednames_fig_1se %in% c(prednames_clim)),
                                                   sum(prednames_fig_1se %in% c(prednames_weath)),
                                                   sum(prednames_fig_1se %in% c(prednames_soils))))
row.names(uniqueCoeffs) <- c("RMSE", "bias: mean(obs-pred.)", "Total number of coefficients", "Number of unique coefficients",
                             "Number of unique climate coefficients", 
                             "Number of unique weather coefficients",  
                             "Number of unique soils coefficients"
                             )

kable(uniqueCoeffs, 
      col.names = c("Best lambda model", "1/2 se lambda model", "1se lambda model"), row.names = TRUE) %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed")) 

	Best lambda model	1/2 se lambda model	1se lambda model
RMSE	0.135	0.137	0.136
bias: mean(obs-pred.)	-6.92e-11	-5.48e-11	-5.16e-11
Total number of coefficients	53	26	33
Number of unique coefficients	13	10	13
Number of unique climate coefficients	6	6	6
Number of unique weather coefficients	3	0	3
Number of unique soils coefficients	4	4	4

Visualizations of Model Predictions and Residuals – using best lambda model

observed vs. predicted values

As the alternative to the best lambda model, use the model (1se or 1/2se of best Lambda) that has the fewest number of unique predictors

if (whichSecondBestMod == "auto") {
  # name of model w/ fewest # of predictors (but more than 0)
uniqueCoeff_min <- min(as.numeric(uniqueCoeffs[4,2:3])[which(as.numeric(uniqueCoeffs[4,2:3]) > 0)])
alternativeModel <- names(uniqueCoeffs[4,2:3])[which(uniqueCoeffs[4,2:3] == uniqueCoeff_min)]

if (is.finite(uniqueCoeff_min)) {
  if (length(alternativeModel) == 1) {
  if (alternativeModel == "X1.2.se.lambda.model") {
  mod_secondBest <- fit_glm_halfse
  name_secondBestMod <- "1/2 SE Model"
  prednames_secondBestMod <- prednames_fig_halfse
} else if (alternativeModel == "X1se.lambda.model") {
  mod_secondBest <- fit_glm_se
  name_secondBestMod <- "1 SE Model"
  prednames_secondBestMod <- prednames_fig_1se
}
} else {
  # if both alternative models have the same number of unique coefficients, chose the model that has the fewest number of total predictors
  uniqueCoeff_min2 <- min(as.numeric(uniqueCoeffs[3,alternativeModel]))
alternativeModel2 <- names(uniqueCoeffs[3,alternativeModel])[which(uniqueCoeffs[3,alternativeModel] == uniqueCoeff_min2)]
# if both models still have the same number of unique coefficeints, chose the 1se lambda model
if (length(alternativeModel2 == 2)) {
  alternativeModel2 <- "X1se.lambda.model"
}
if (alternativeModel2 == "X1.2.se.lambda.model") {
  mod_secondBest <- fit_glm_halfse
  name_secondBestMod <- "1/2 SE Model"
  prednames_secondBestMod <- prednames_fig_halfse
} else if (alternativeModel2 == "X1se.lambda.model") {
  mod_secondBest <- fit_glm_se
  name_secondBestMod <- "1 SE Model"
  prednames_secondBestMod <- prednames_fig_1se
}
}
  }else {
    mod_secondBest <- NULL
  name_secondBestMod <- "Intercept_Only"
  prednames_secondBestMod <- NULL
}
} else if (whichSecondBestMod == "1se") {
  mod_secondBest <- fit_glm_se
  name_secondBestMod <- "1 SE Model"
  prednames_secondBestMod <- prednames_fig_1se
} else if (whichSecondBestMod == "halfse") {
  mod_secondBest <- fit_glm_halfse
  name_secondBestMod <- "1/2 SE Model"
  prednames_secondBestMod <- prednames_fig_halfse
}

Predicting on the data

  # create prediction for each each model
# (i.e. for each fire proporation variable)
predict_by_response <- function(mod, df) {
  df_out <- df
  response_name <- paste0(response, "_pred")
  preds <- predict(mod, newx= df_out, #s="lambda.min", 
                                     type = "response")
  preds[preds<0] <- 0
  #preds[preds>100] <- 100
  df_out <- df_out %>% cbind(preds)
   colnames(df_out)[ncol(df_out)] <- response_name
  return(df_out)
}

pred_glm1 <- predict_by_response(fit_glm_bestLambda, X[,2:ncol(X)])

## back-transform the 
# add back in true y values
pred_glm1 <- pred_glm1 %>% 
  cbind(data.frame(response = modDat_1_s[,c(response)])) 
names(pred_glm1)[names(pred_glm1) == "response"] <- response

# add back in lat/long data 
pred_glm1 <- pred_glm1 %>% 
  cbind(modDat_1_s[,c("x", "y", "Year")])

pred_glm1$resid  <- pred_glm1[,response] - pred_glm1[,paste0(response, "_pred")]
pred_glm1$extremeResid <- NA
pred_glm1[pred_glm1$resid > 1 | pred_glm1$resid < 1,"extremeResid"] <- 1

if ( name_secondBestMod == "Intercept_Only") {
  print("The next best lambda model only contains one predictor (an intercept)")
} else {

pred_glm1_1se <- predict_by_response(mod_secondBest, X[,2:ncol(X)])

# add back in true y values
pred_glm1_1se <- pred_glm1_1se %>% 
  cbind(data.frame(response = modDat_1_s[,c(response)])) 
names(pred_glm1_1se)[names(pred_glm1_1se) == "response"] <- response

# add back in lat/long data 
pred_glm1_1se <- pred_glm1_1se %>% 
  cbind(modDat_1_s[,c("x", "y", "Year")])

pred_glm1_1se$resid <- pred_glm1_1se[,response] - pred_glm1_1se[,paste0(response, "_pred")]
pred_glm1_1se$extremeResid <- NA
pred_glm1_1se[pred_glm1_1se$resid > 1 | pred_glm1_1se$resid < -1,"extremeResid"] <- 1
}

Maps of Observations, Predictions, and Residuals=

Observations across the temporal range of the dataset

# rasterize
# get reference raster
# use the gridMet raster 
test_rast_dayMet <- rast("../../../Data_raw/dayMet/rawMonthlyData/orders/70e0da02b9d2d6e8faa8c97d211f3546/Daymet_Monthly_V4R1/data/daymet_v4_prcp_monttl_na_1980.tif") %>%
  #terra::project(terra::crs("EPSG:4326")) %>%
  terra::crop(ext(-2000000, 2600000, -1900000, 1500000))

## aggregate to a 4x4km^2 grid
test_rast <- test_rast_dayMet %>% 
  terra::aggregate(fact = 8, fun = "mean")
# test_rast_Untranfsormed <-  rast("../../../Data_raw/gridMet/pr_2020.nc") #%>% ## mean cell size of unaggregated grid size (16709380m^2)
# test_rast <- test_rast_Untranfsormed %>% 
#    terra::aggregate(fact = 2, fun = "mean") #%>% 
regions <- sf::st_read(dsn = "../../../Data_raw/Level2Ecoregions/", layer = "NA_CEC_Eco_Level2") 

## Reading layer `NA_CEC_Eco_Level2' from data source 
##   `/Users/astears/Documents/Dropbox_static/Work/NAU_USGS_postdoc/cleanPED/PED_vegClimModels/Data_raw/Level2Ecoregions' 
##   using driver `ESRI Shapefile'
## Simple feature collection with 2261 features and 8 fields
## Geometry type: POLYGON
## Dimension:     XY
## Bounding box:  xmin: -4334052 ymin: -3313739 xmax: 3324076 ymax: 4267265
## Projected CRS: Sphere_ARC_INFO_Lambert_Azimuthal_Equal_Area

regions <- regions %>% 
  st_transform(crs = st_crs(crs(test_rast))) %>% 
  st_make_valid() 

# ecoregionLU <- data.frame("NA_L1NAME" = sort(unique(regions$NA_L1NAME)), 
#                         "newRegion" = c(NA, "Forest", "dryShrubGrass", 
#                                         "dryShrubGrass", "Forest", "dryShrubGrass",
#                                        "dryShrubGrass", "Forest", "Forest", 
#                                        "dryShrubGrass", "Forest", "Forest", 
#                                        "Forest", "Forest", "dryShrubGrass", 
#                                        NA
#                                         ))
# goodRegions <- regions %>% 
#   left_join(ecoregionLU)
# mapRegions <- goodRegions %>% 
#   filter(!is.na(newRegion)) %>% 
#   group_by(newRegion) %>% 
#   summarise(geometry = sf::st_union(geometry)) %>% 
#   ungroup() %>% 
#   st_simplify(dTolerance = 1000) %>% 
#   sf::st_crop(c("xmin" = -2000000, "xmax" = 2600000, "ymin" = -1900000, "ymax" = 1500000))
# make shapefile of cropped state boundaries in appropriate crs
cropped_states_2 <- cropped_states %>% 
  st_transform(crs = crs(test_rast)) %>% 
  st_make_valid()  %>% 
  sf::st_crop(c("xmin" = -2000000, "xmax" = 2600000, "ymin" = -1900000, "ymax" = 1500000))

# make a multi-layer raster w/ layers for each variable of interest
pred_glm1_sf <- pred_glm1 %>% 
  st_as_sf(coords = c("x", "y"), crs = crs("EPSG:4326")) %>% 
  st_transform(crs(test_rast)) %>% 
  terra::vect()

# rasterize the observations and predictions
testRast2 <- lapply(c(response, paste0(response, "_pred"), "resid"), FUN = function(x) {
  # S4 method for class 'data.frame'
temp <- terra::rasterize(x = pred_glm1_sf, y = test_rast, 
                         field = x, fun = mean, na.rm = TRUE)
names(temp) <- x
  # rast(pred_glm1_full[,c("x", "y", x)] %>% drop_na(), type="xyz", crs=terra::crs(test_rast$`precipitation_amount_day=43829`), digits=6, extent=test_rast$`precipitation_amount_day=43829`)
 return(temp)
  }
)
pred_glm1_RAST <- c(testRast2[[1]], testRast2[[2]], testRast2[[3]])

# ## compare
# par(mfrow = c(2,1))
# terra::plot(pred_glm1_RAST$TotalTreeCover,  maxcell = 30000000, main = "gridMet")
# terra::plot(pred_glm1_RAST_dayMet$TotalTreeCover, maxcell = 30000000, main = "dayMet")
# par(mfrow = c(1,1))
##
# make figure of observations
map_obs <- ggplot() +
geom_spatraster(data = pred_glm1_RAST, aes(fill = .data[[response]]), maxcell = 50000000) + 
 #geom_sf(data = pred_glm1_RAST, aes(col = TotalTreeCover)) + 
  # stat_summary_2d(data = plotObs, aes(x = x, y = y, z = TotalTreeCover), fun = mean, binwidth = .05) + 
  geom_sf(data=cropped_states_2 ,fill=NA ) +
labs(title = paste0("Observations of ", response, " in the ",ecoregion, " ecoregion")) +
  scale_fill_gradient2(low = "brown",
                       mid = "wheat" ,
                       high = "forestgreen" , 
                       midpoint = 0,   na.value = "white") + 
  coord_sf(datum = st_crs(pred_glm1_RAST)) +
   # xlim(-104, -100) + 
   # ylim(30, 33)
  xlim(-2000000, 2500000) + 
  ylim(-1800000, 900000)
# histogram of observations
hist_obs <- pred_glm1%>% 
  ggplot() + 
  geom_histogram(aes(.data[[response]]), fill = "lightgrey", col = "darkgrey")

library(ggpubr)
ggarrange( map_obs, hist_obs, heights = c(3, 1), ncol = 1)

# 
# # rasterize
# # get reference raster
# test_rast <-  rast("../../../Data_raw/dayMet/rawMonthlyData/orders/70e0da02b9d2d6e8faa8c97d211f3546/Daymet_Monthly_V4R1/data/daymet_v4_prcp_monttl_na_1980.tif") %>% 
#   terra::aggregate(fact = 8, fun = "mean")
# ## add ecoregion boundaries (for our ecoregion level model)
# regions <- sf::st_read(dsn = "../../../Data_raw/Level2Ecoregions/", layer = "NA_CEC_Eco_Level2") 
# regions <- regions %>% 
#   st_transform(crs = st_crs(test_rast)) %>% 
#   st_make_valid() 
# 
# ecoregionLU <- data.frame("NA_L1NAME" = sort(unique(regions$NA_L1NAME)), 
#                         "newRegion" = c(NA, "Forest", "dryShrubGrass", 
#                                         "dryShrubGrass", "Forest", "dryShrubGrass",
#                                        "dryShrubGrass", "Forest", "Forest", 
#                                        "dryShrubGrass", "Forest", "Forest", 
#                                        "Forest", "Forest", "dryShrubGrass", 
#                                        NA
#                                         ))
# goodRegions <- regions %>% 
#   left_join(ecoregionLU)
# mapRegions <- goodRegions %>% 
#   filter(!is.na(newRegion)) %>% 
#   group_by(newRegion) %>% 
#   summarise(geometry = sf::st_union(geometry)) %>% 
#   ungroup() %>% 
#   st_simplify(dTolerance = 1000)
# #mapview(mapRegions)
# # rasterize data
# plotObs <- pred_glm1 %>% 
#          drop_na(paste(response)) %>% 
#   #slice_sample(n = 5e4) %>%
#   terra::vect(geom = c("Long", "Lat")) %>% 
#   terra::set.crs(crs(test_rast)) %>% 
#   terra::rasterize(y = test_rast, 
#                    field = response, 
#                    fun = mean) #%>% 
#   #terra::aggregate(fact = 2, fun = mean, na.rm = TRUE) %>% 
#   #terra::crop(ext(-1950000, 1000000, -1800000, 1000000))
# 
# # get the extent of this particular raster, and crop it accordingly
# tempExt <- crds(plotObs, na.rm = TRUE)
# 
# plotObs_2 <- plotObs %>% 
#   crop(ext(min(tempExt[,1]), max(tempExt[,1]),
#            min(tempExt[,2]), max(tempExt[,2])) 
#        )
# # make figures
# map_obs <- ggplot() +
# geom_spatraster(data = plotObs_2) + 
#   geom_sf(data=cropped_states %>% st_transform(crs = st_crs(test_rast)) %>% st_crop(st_bbox(plotObs_2)),fill=NA ) +
#   geom_sf(data = mapRegions, fill = NA, col = "orchid", lwd = .5) +
# labs(title = paste0("Observations of ", response, " in the ",ecoregion, " ecoregion")) +
#   scale_fill_gradient2(low = "brown",
#                        mid = "wheat" ,
#                        high = "darkgreen" , 
#                        midpoint = 0,   na.value = "grey20") + 
#   xlim(st_bbox(plotObs_2)[c(1,3)]) + 
#   ylim(st_bbox(plotObs_2)[c(2,4)])
# 
# hist_obs <- ggplot(pred_glm1) + 
#   geom_histogram(aes(.data[[response]]), fill = "lightgrey", col = "darkgrey")
# 
# library(ggpubr)
# ggarrange(map_obs, hist_obs, heights = c(3,1), ncol = 1)

Predictions across the temporal range of the dataset

map_preds1 <- ggplot() +
geom_spatraster(data = pred_glm1_RAST, aes(fill = .data[[paste0(response,"_pred")]]), maxcell = 50000000) +
  #geom_sf(data = highPred_points, col = "red") +
geom_sf(data=cropped_states_2 ,fill=NA ) +
  labs(title = paste0("Predictions from the 'best lambda' fitted model of ", response, " in the ",ecoregion, " ecoregion"),
     subtitle =  "bestLambda model")  +
  scale_fill_gradient2(low = "wheat",
                       mid = "darkgreen",
                       high = "red" , 
                       midpoint = 1,   na.value = "white",
                       limits = c(0,1)) + 
  xlim(-2000000, 2500000) + 
  ylim(-1800000, 900000)

hist_preds1 <- ggplot(pred_glm1) + 
  geom_histogram(aes(.data[[paste0(response, "_pred")]]), fill = "lightgrey", col = "darkgrey")+ 
  xlim(c(0,1))

ggarrange(map_preds1, hist_preds1, heights = c(3,1), ncol = 1)

if ( name_secondBestMod == "Intercept_Only") {
  print("The next best lambda model only contains one predictor (an intercept)")
} else {

# rasterize data
# make a multi-layer raster w/ layers for each variable of interest
pred_glm1_1se_sf <- pred_glm1_1se %>% 
  st_as_sf(coords = c("x", "y"), crs = crs("EPSG:4326")) %>% 
  st_transform(crs(test_rast)) %>% 
  terra::vect()

# rasterize the observations and predictions
testRast3 <- lapply(c(response, paste0(response, "_pred"), "resid"), FUN = function(x) {
  # S4 method for class 'data.frame'
temp <- terra::rasterize(x = pred_glm1_1se_sf, y = test_rast, 
                         field = x, fun = mean, na.rm = TRUE)
names(temp) <- x
  # rast(pred_glm1_full[,c("x", "y", x)] %>% drop_na(), type="xyz", crs=terra::crs(test_rast$`precipitation_amount_day=43829`), digits=6, extent=test_rast$`precipitation_amount_day=43829`)
 return(temp)
  }
)
pred_glm1_1se_RAST <- c(testRast3[[1]], testRast3[[2]], testRast3[[3]])

# make figures
map_preds2 <- ggplot() +
geom_spatraster(data = pred_glm1_RAST, aes(fill = .data[[paste0(response,"_pred")]]), maxcell = 50000000) + 
 geom_sf(data=cropped_states_2 ,fill=NA ) +
labs(title = paste0("Predictions from the ", name_secondBestMod, "fitted model of ", response, " in the ",ecoregion, " ecoregion"),
     subtitle =  name_secondBestMod)  +
  scale_fill_gradient2(low = "wheat",
                       mid = "darkgreen",
                       high = "red" , 
                       midpoint = 1,   na.value = "white",
                       limits = c(0, 1)) +
  xlim(-2000000, 2500000) + 
  ylim(-1800000, 900000)


hist_preds2 <- ggplot(pred_glm1_1se) + 
  geom_histogram(aes(.data[[paste0(response, "_pred")]]), fill = "lightgrey", col = "darkgrey")+ 
  xlim(c(0,1))

ggarrange(map_preds2, hist_preds2, heights = c(3,1), ncol = 1)
}

# identify locations where residuals are >100 or < -100
badResids_high <- pred_glm1 %>% 
  filter(resid > .5)  %>% 
  terra::vect(geom = c("x", "y")) %>% 
  terra::set.crs(crs("EPSG:4326")) %>% 
  terra::project(crs(test_rast))
badResids_low <- pred_glm1 %>% 
  filter(resid < -.5)  %>% 
  terra::vect(geom = c("x", "y")) %>% 
  terra::set.crs(crs("EPSG:4326")) %>% 
  terra::project(crs(test_rast))
# make figures
map <- ggplot() +
geom_spatraster(data = pred_glm1_RAST, aes(fill = resid), maxcell = 50000000) + 
  geom_sf(data=cropped_states_2 ,fill=NA ) +
  geom_sf(data = badResids_high, col = "blue") +
  geom_sf(data = badResids_low, col = "red") +
labs(title = paste0("Resids. (obs. - pred.) from the ", ecoregion," ecoregion-wide model of ", response),
     subtitle = "bestLambda model \n red points indicate locations that have residuals below -0.5 \n blue points indicate locations that have residuals above 0.5") +
  scale_fill_gradient2(low = "red",
                       mid = "white" ,
                       high = "blue" , 
                       midpoint = 0,   na.value = "grey30",
                       limits = c(-1,1)
                       ) +
  xlim(-2000000, 2500000) + 
  ylim(-1800000, 900000)

hist <- ggplot(pred_glm1) + 
  geom_histogram(aes(resid), fill = "lightgrey", col = "darkgrey") + 
  geom_text(aes(x = min(resid)*.9, y = 1500, label = paste0("min = ", round(min(resid),2)))) +
  geom_text(aes(x = max(resid)*.9, y = 1500, label = paste0("max = ", round(max(resid),2)))) + 
  geom_vline(aes(xintercept = mean(resid)))

ggarrange(map, hist, heights = c(3,1), ncol = 1)

if ( name_secondBestMod == "Intercept_Only") {
  print("The next best lambda model only contains one predictor (an intercept)")
} else {

# identify locations where residuals are >100 or < -100
badResids_high <- pred_glm1_1se %>% 
  filter(resid > .5)  %>% 
  terra::vect(geom = c("x", "y")) %>% 
  terra::set.crs(crs("EPSG:4326")) %>% 
  terra::project(crs(test_rast))
badResids_low <- pred_glm1_1se %>% 
  filter(resid < -.5)  %>% 
  terra::vect(geom = c("x", "y")) %>% 
  terra::set.crs(crs("EPSG:4326")) %>% 
  terra::project(crs(test_rast))
# make figures
map <- ggplot() +
geom_spatraster(data = pred_glm1_1se_RAST, aes(fill = resid), maxcell = 50000000) + 
  geom_sf(data=cropped_states_2 ,fill=NA ) +
  geom_sf(data = badResids_high, col = "blue") +
  geom_sf(data = badResids_low, col = "red") +
labs(title = paste0("Resids. (obs. - pred.) from the ", ecoregion," ecoregion-wide model of ", response),
     subtitle = "bestLambda model \n red points indicate locations that have residuals below -0.5 \n blue points indicate locations that have residuals above 0.5") +
  scale_fill_gradient2(low = "red",
                       mid = "white" ,
                       high = "blue" , 
                       midpoint = 0,   na.value = "grey30",
                       limits = c(-1,1)
                       ) +
  xlim(-2000000, 2500000) + 
  ylim(-1800000, 900000)

hist <- ggplot(pred_glm1_1se) + 
  geom_histogram(aes(resid), fill = "lightgrey", col = "darkgrey") + 
  geom_text(aes(x = min(resid)*.9, y = 1500, label = paste0("min = ", round(min(resid),2)))) +
  geom_text(aes(x = max(resid)*.9, y = 1500, label = paste0("max = ", round(max(resid),2)))) + 
  geom_vline(aes(xintercept = mean(resid)))

ggarrange(map, hist, heights = c(3,1), ncol = 1)

}

Are there biases of the model predictions across year/lat/long?

if ( name_secondBestMod == "Intercept_Only") {
  print("The next best lambda model only contains one predictor (an intercept)")
  # plot residuals against Year
yearResidMod_bestLambda <- ggplot(pred_glm1) + 
  geom_point(aes(x = jitter(Year), y = resid), alpha = .1) + 
  geom_smooth(aes(x = Year, y = resid)) + 
  xlab("Year") + 
  ylab("Residuals") +
  ggtitle("from best lamba model")

# plot residuals against Lat
latResidMod_bestLambda <- ggplot(pred_glm1) + 
  geom_point(aes(x = y, y = resid), alpha = .1) + 
  geom_smooth(aes(x = y, y = resid)) + 
  xlab("Latitude") + 
  ylab("Residuals") +
  ggtitle("from best lamba model")

# plot residuals against Long
longResidMod_bestLambda <- ggplot(pred_glm1) + 
  geom_point(aes(x = x, y = resid), alpha = .1) + 
  geom_smooth(aes(x = x, y = resid)) + 
  xlab("Longitude") + 
  ylab("Residuals") +
  ggtitle("from best lamba model")
library(patchwork)
(yearResidMod_bestLambda ) / 
(  latResidMod_bestLambda ) /
(  longResidMod_bestLambda )
} else {

# plot residuals against Year
yearResidMod_bestLambda <- ggplot(pred_glm1) + 
  geom_point(aes(x = jitter(Year), y = resid), alpha = .1) + 
  geom_smooth(aes(x = Year, y = resid)) + 
  xlab("Year") + 
  ylab("Residuals") +
  ggtitle("from best lamba model")
yearResidMod_1seLambda <- ggplot(pred_glm1_1se) + 
  geom_point(aes(x = jitter(Year), y = resid), alpha = .1) + 
  geom_smooth(aes(x = Year, y = resid)) + 
  xlab("Year") + 
  ylab("Residuals") +
  ggtitle(paste0("from ", name_secondBestMod))

# plot residuals against Lat
latResidMod_bestLambda <- ggplot(pred_glm1) + 
  geom_point(aes(x = y, y = resid), alpha = .1) + 
  geom_smooth(aes(x = y, y = resid)) + 
  xlab("Latitude") + 
  ylab("Residuals") +
  ggtitle("from best lamba model")
latResidMod_1seLambda <- ggplot(pred_glm1_1se) + 
  geom_point(aes(x = y, y = resid), alpha = .1) + 
  geom_smooth(aes(x = y, y = resid)) + 
  xlab("Latitude") + 
  ylab("Residuals") +
  ggtitle(paste0("from ", name_secondBestMod))

# plot residuals against Long
longResidMod_bestLambda <- ggplot(pred_glm1) + 
  geom_point(aes(x = x, y = resid), alpha = .1) + 
  geom_smooth(aes(x = x, y = resid)) + 
  xlab("Longitude") + 
  ylab("Residuals") +
  ggtitle("from best lamba model")
longResidMod_1seLambda <- ggplot(pred_glm1_1se) + 
  geom_point(aes(x = x, y = resid), alpha = .1) + 
  geom_smooth(aes(x = x, y = resid)) + 
  xlab("Longitude") + 
  ylab("Residuals") +
  ggtitle(paste0("from ", name_secondBestMod))

library(patchwork)
(yearResidMod_bestLambda + yearResidMod_1seLambda) / 
(  latResidMod_bestLambda + latResidMod_1seLambda) /
(  longResidMod_bestLambda + longResidMod_1seLambda)
}

Quantile plots

Binning predictor variables into “Quantiles” and looking at the mean predicted probability for each percentile.

# get deciles for best lambda model 
if (length(prednames_fig) == 0) {
  print("The best lambda model only contains one predictor (an intercept), so decile plots aren't possible to generate")
} else {
  pred_glm1_deciles <- predvars2deciles(pred_glm1,
                                      response_vars = response_vars,
                                        pred_vars = prednames_fig, 
                                       cut_points = seq(0, 1, 0.01))
}
# get deciles for 1 SE lambda model 
if ( name_secondBestMod == "Intercept_Only") {
  print("The next best lambda model only contains one predictor (an intercept)")} else {
  pred_glm1_deciles_1se <- predvars2deciles(pred_glm1_1se,
                                      response_vars = response_vars,
                                        pred_vars = prednames_secondBestMod, 
                                       cut_points = seq(0, 1, 0.01))
  }

Below are quantile plots for the best lambda model (note that the predictor variables are scaled)

if (length(prednames_fig) == 0) {
  print("The model only contains one predictor (an intercept), so decile plots aren't possible to generate")
} else {

# publication quality version
g3 <- decile_dotplot_pq(df = pred_glm1_deciles, response = c(response, paste0(response, "_pred")), IQR = TRUE,
                        CI = FALSE
                        ) + ggtitle("Decile Plot")

g4 <- add_dotplot_inset(g3, df = pred_glm1_deciles, response = c(response, paste0(response, "_pred")), dfRaw = pred_glm1, add_smooth = TRUE, deciles = FALSE)

  
if(save_figs) {
  # png(paste0("../../../Figures/CoverDatFigures/ figures/quantile_plots/quantile_plot_", response,  "_",ecoregion,".png"), 
  #    units = "in", res = 600, width = 5.5, height = 3.5 )
  #   print(g4)
  # dev.off()
}

g4
}

Below are percentile plots from the second best lambda model ()

if ( name_secondBestMod == "Intercept_Only") {
  print("The next best lambda model only contains one predictor (an intercept)")
  } else {

# publication quality version
g3 <- decile_dotplot_pq(pred_glm1_deciles_1se, response = c(response, paste0(response, "_pred")), IQR = TRUE) + ggtitle("Decile Plot")

g4 <- add_dotplot_inset(g3, df = pred_glm1_deciles_1se, response = c(response, paste0(response, "_pred")), dfRaw = pred_glm1_1se, add_smooth = TRUE, deciles = FALSE)

  
if(save_figs) {
  # png(paste0("figures/quantile_plots/quantile_plot_", response,  "_",ecoregion,".png"), 
  #    units = "in", res = 600, width = 5.5, height = 3.5 )
  #   print(g4)
  # dev.off()
}

g4
}

Filtered Quantiles

For the best lambda model

Filtered ‘Quantile’ plots of data. These plots show each vegetation variable, but only based on data that falls into the upper and lower 20th percentiles of each predictor variable.

if (length(prednames_fig) == 0) {
  print("The model only contains one predictor (an intercept), so decile plots aren't possible to generate")
} else {
pred_glm1_deciles_filt <- predvars2deciles( pred_glm1, 
                         response_vars = c(response, paste0(response, "_pred")),
                         pred_vars = prednames_fig,
                         filter_var = TRUE,
                         filter_vars = prednames_fig,
                         cut_points = seq(0, 1, 0.01)) 
g <- decile_dotplot_filtered_pq(df = pred_glm1_deciles_filt, response = response, 
                                xvars = prednames_fig)

if(save_figs) {
# jpeg(paste0("figures/quantile_plots/quantile_plot_filtered_mid_v1", , ".jpeg"),
#      units = "in", res = 600, width = 5.5, height = 6 )
#   g 
# dev.off()
}
g
}

Filtered quantile figure with middle 2 deciles also shown

if ( name_secondBestMod == "Intercept_Only") {
  print("The next best lambda model only contains one predictor (an intercept)")
} else {
pred_glm1_deciles_filt_mid <- predvars2deciles(pred_glm1, 
                         response_vars = c(response, paste0(response, "_pred")),
                         pred_vars = prednames_fig,
                         filter_vars = prednames_fig,
                         filter_var = TRUE,
                         add_mid = TRUE,
                         cut_points = seq(0, 1, 0.01))

g <- decile_dotplot_filtered_pq(df = pred_glm1_deciles_filt_mid, response = response, 
                                xvars = prednames_fig)

if(save_figs) {
# jpeg(paste0("figures/quantile_plots/quantile_plot_filtered_mid_v1", , ".jpeg"),
#      units = "in", res = 600, width = 5.5, height = 6)
#   g 
# dev.off()
}
g
}

For the second best lambda model ()

Filtered ‘Quantile’ plots of data. These plots show each vegetation variable, but only based on data that falls into the upper and lower 20th percentiles of each predictor variable.

if (length(prednames_secondBestMod) == 0) {
  print("The model only contains one predictor (an intercept), so decile plots aren't possible to generate")
} else {
  
pred_glm1_deciles_filt <- predvars2deciles( pred_glm1_1se, 
                         response_vars = c(response, paste0(response, "_pred")),
                         pred_vars = prednames_secondBestMod,
                         filter_var = TRUE,
                         filter_vars = prednames_secondBestMod,
                         cut_points = seq(0, 1, 0.01)) 
g <- decile_dotplot_filtered_pq(df = pred_glm1_deciles_filt, response = response, 
                                xvars = prednames_fig)

if(save_figs) {
# jpeg(paste0("figures/quantile_plots/quantile_plot_filtered_mid_v1", , ".jpeg"),
#      units = "in", res = 600, width = 5.5, height = 6 )
#   g 
# dev.off()
}
g
}

Filtered quantile figure with middle 2 deciles also shown

if (length(prednames_secondBestMod) == 0) {
  print("The model only contains one predictor (an intercept), so decile plots aren't possible to generate")
} else {
pred_glm1_deciles_filt_mid <- predvars2deciles(pred_glm1, 
                         response_vars = c(response, paste0(response, "_pred")),
                         pred_vars = prednames_secondBestMod,
                         filter_vars = prednames_secondBestMod,
                         filter_var = TRUE,
                         add_mid = TRUE,
                         cut_points = seq(0, 1, 0.01))

g <- decile_dotplot_filtered_pq(df = pred_glm1_deciles_filt_mid, response = response, 
                                xvars = prednames_fig)


if(save_figs) {
# jpeg(paste0("figures/quantile_plots/quantile_plot_filtered_mid_v1", , ".jpeg"),
#      units = "in", res = 600, width = 5.5, height = 6 )
#   g 
# dev.off()
}
g
}

Show model RMSE w/in each quantile

# get deciles for best lambda model 
if (length(prednames_fig) == 0) {
  print("The best lambda model only contains one predictor (an intercept), so decile plots aren't possible to generate")
} else {
  pred_glm1_deciles %>% 
    ggplot(aes(x = mean_value, y = RMSE)) +
    facet_wrap(~name, scales = "free_x") +
    geom_point(alpha = .2, size = .5) + 
    geom_smooth(lwd = .5) + 
    xlab("Scaled predictor value") + 
    ggtitle("RMSE by decile for bestLambda model")
}

# get deciles for 1 SE lambda model 
if (length(prednames_secondBestMod) == 0) {
  print("The 1SE (or 1/2 SE) lambda model only contains one predictor (an intercept), so decile plots aren't possible to generate")
} else {
  pred_glm1_deciles_1se %>% 
    ggplot(aes(x = mean_value, y = RMSE)) +
    facet_wrap(~name, scales = "free_x") +
    geom_point(alpha = .2, size = .5) + 
    geom_smooth(lwd = .5) + 
    xlab("Scaled predictor value") + 
    ggtitle(paste0("RMSE by decile for ", name_secondBestMod, "model"))
}

Cross-validation

Using best lambda model

Use terms from global model to re-fit and predict on different held out regions

Figures show residuals for each of the models fit to held-out ecoregions

These models were fit to six ecoregions, and then predict on the indicated heldout ecoregion

if (length(prednames_fig) == 0) {
  print("The model only contains one predictor (an intercept), so cross validation isn't practical")
} else {

## code from Tredennick et al. 2020
# try each separate level II ecoregion as a test set
# make a list to hold output data
outList <- vector(mode = "list", length = length(sort(unique(modDat_1_s$NA_L2NAME))))
# obs_pred <- data.frame(ecoregion = character(),obs = numeric(),
#                        pred_opt = numeric(), pred_null = numeric()#,
#                        #pred_nopenalty = numeric()
#                        )

## get the model specification from the global model
mat <- as.matrix(coef(fit_glm_bestLambda, s = "lambda.min"))
mat2 <- mat[mat[,1] != 0,]

f_cv <- as.formula(paste0(response, " ~ ", paste0(names(mat2)[2:length(names(mat2))], collapse = " + ")))

X_cv <- model.matrix(object = f_cv, data = modDat_1_s)
# get response variable
y_cv <- as.matrix(modDat_1_s[,response])


# now, loop through so with each iteration, a different ecoregion is held out
 for(i_eco in sort(unique(modDat_1_s$NA_L2NAME))){

  # split into training and test sets
  test_eco <- i_eco
  print(test_eco)
  # identify the rowID of observations to be in the training and test datasets
  train <- which(modDat_1_s$NA_L2NAME!=test_eco) # data for all ecoregions that aren't 'i_eco'
  test <- which(modDat_1_s$NA_L2NAME==test_eco) # data for the ecoregion that is 'i_eco'

  trainDat_all <- modDat_1_s %>%
    slice(train) %>%
    dplyr::select(-newRegion)
  testDat_all <- modDat_1_s %>%
    slice(test) %>%
    dplyr::select(-newRegion)

  # get the model matrices for input and response variables for cross validation model specification
  X_train <- as.matrix(X_cv[train,])
  X_test <- as.matrix(X_cv[test,])

  y_train <- modDat_1_s[train,response]
  y_test <- modDat_1_s[test,response]

  # get the model matrices for input and response variables for original model specification
  X_train_glob <- as.matrix(X[train,])
  X_test_glob <- as.matrix(X[test,])

  y_train_glob <- modDat_1_s[train,response]
  y_test_glob <- modDat_1_s[test,response]

  train_eco <- modDat_1_s$NA_L2NAME[train]

  ## just try a regular glm w/ the components from the global model
  fit_i <- glm(data = trainDat_all, formula = f_cv,
    ,
               family =  quasibeta_family(link = "logit")
    )
    
  # lasso model predictions with the optimal lambda (back transformed)
  optimal_pred <- predict(fit_i, newdata= testDat_all, type = "response") 
  # null model and predictions
  # the "null" model in this case is the global model
  # predict on the test data for this iteration w/ the global model (back transformed)
  null_pred <- predict.glm(fit_glm_bestLambda, newdata = testDat_all, type = "response") 


  # save data
  tmp <- data.frame(ecoRegion_holdout = rep(test_eco,length(y_test)),
                    obs=y_test,
                    pred_opt=optimal_pred,
                    pred_null=null_pred#,
                    #pred_nopenalty=nopen_pred
                    ) %>%
    cbind(testDat_all)

  # calculate RMSE, bias, etc. of
  # RMSE of CV model
  RMSE_optimal <- yardstick::rmse(data = data.frame(optimal_pred,"y_test" = (y_test)), truth = "y_test", estimate = "optimal_pred")[1,]$.estimate
  # RMSE of global model
  RMSE_null <- yardstick::rmse(data = data.frame(null_pred,"y_test" = (y_test)), truth = "y_test", estimate = "null_pred")[1,]$.estimate
  # bias of CV model
  bias_optimal <- mean((y_test) - optimal_pred)
  # bias of global model
  bias_null <-  mean((y_test) - null_pred )

  # put output into a list
  tmpList <- list("testRegion" = i_eco,
    "modelObject" = fit_i,
       "modelPredictions" = tmp,
    "performanceMetrics" = data.frame("RMSE_cvModel" = RMSE_optimal,
                                      "RMSE_globalModel" = RMSE_null,
                                      "bias_cvModel" = bias_optimal,
                                      "bias_globalModel" = bias_null))

  # save model outputs
  outList[[which(sort(unique(modDat_1_s$NA_L2NAME)) == i_eco)]] <- tmpList
 }
}

## [1] "COLD DESERTS"
## [1] "MARINE WEST COAST FOREST"
## [1] "MEDITERRANEAN CALIFORNIA"
## [1] "MIXED WOOD PLAINS"
## [1] "MIXED WOOD SHIELD"
## [1] "SOUTH CENTRAL SEMIARID PRAIRIES"
## [1] "SOUTHEASTERN USA PLAINS AND EVERGLADES AND LOUISIANA PLAIN"
## [1] "TEMPERATE PRAIRIES"
## [1] "UPPER GILA MOUNTAINS"
## [1] "WARM DESERTS"
## [1] "WEST-CENTRAL SEMIARID PRAIRIES"
## [1] "WESTERN CORDILLERA"
## [1] "WESTERN SIERRA MADRE PIEDMONT"

Below are the RMSE and bias values for predictions made for each holdout level II ecoregion, compared to predictions from the global model for that same ecoregion

# table of model performance
purrr::map(outList, .f = function(x) {
  cbind(data.frame("holdout region" = x$testRegion),  x$performanceMetrics)
}
) %>%
  purrr::list_rbind() %>%
  kable(col.names = c("Held-out ecoregion", "RMSE of CV model", "RMSE of global model",
                      "bias of CV model - mean(obs-pred.)", "bias of global model- mean(obs-pred.)"),
        caption = "Performance of Cross Validation using 'best lambda' model specification") %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"))

Performance of Cross Validation using ‘best lambda’ model specification

Held-out ecoregion	RMSE of CV model	RMSE of global model	bias of CV model - mean(obs-pred.)	bias of global model- mean(obs-pred.)
COLD DESERTS	0.1850834	0.1324363	-0.1018408	-0.0158007
MARINE WEST COAST FOREST	0.5049667	0.5031583	-0.4646057	-0.4626473
MEDITERRANEAN CALIFORNIA	0.2688935	0.1882978	0.1917655	0.0506605
MIXED WOOD PLAINS	0.3157740	0.3080396	-0.2620992	-0.2525331
MIXED WOOD SHIELD	0.3093063	0.3028675	0.0304719	0.0132120
SOUTH CENTRAL SEMIARID PRAIRIES	0.1650745	0.1324572	0.0712403	0.0149529
SOUTHEASTERN USA PLAINS AND EVERGLADES AND LOUISIANA PLAIN	0.2009903	0.1440180	0.0629266	0.0042154
TEMPERATE PRAIRIES	0.3096520	0.2222351	-0.2504182	-0.1335821
UPPER GILA MOUNTAINS	0.1564841	0.1532443	-0.0581575	-0.0521315
WARM DESERTS	0.1323415	0.1005595	-0.0519839	-0.0082085
WEST-CENTRAL SEMIARID PRAIRIES	0.2073899	0.1216422	0.1661051	0.0363379
WESTERN CORDILLERA	0.2498107	0.2162761	-0.0951198	-0.0436121
WESTERN SIERRA MADRE PIEDMONT	0.1518154	0.1410581	0.0967432	0.0806991

# visualize model predictions
for (i in 1:length(unique(modDat_1_s$NA_L2NAME))) {
  holdoutRegion <- outList[[i]]$testRegion
  predictionData <- outList[[i]]$modelPredictions
  modTerms <- as.matrix(coef(outList[[i]]$modelObject)) %>%
    as.data.frame() %>%
    filter(V1!=0) %>%
    rownames()

  # calculate residuals
  predictionData <- predictionData %>%
  mutate(resid = .[["obs"]] - .[["pred_opt"]] ,
         resid_globMod = .[["obs"]]  - .[["pred_null"]])


# rasterize
# use 'test_rast' from earlier

  # rasterize data
plotObs <- predictionData %>%
         drop_na(paste(response)) %>%
  #slice_sample(n = 5e4) %>%
  terra::vect(geom = c("x", "y")) %>%
  terra::set.crs(crs("EPSG:4326")) %>%
  terra::project(crs(test_rast)) %>%
  terra::rasterize(y = test_rast,
                   field = "resid",
                   fun = mean) #%>%
  #terra::aggregate(fact = 2, fun = mean, na.rm = TRUE) %>%
  #terra::crop(ext(-1950000, 1000000, -1800000, 1000000))

tempExt <- crds(plotObs, na.rm = TRUE)
plotObs_2 <- plotObs %>%  
  crop(ext(min(tempExt[,1]), max(tempExt[,1]),
           min(tempExt[,2]), max(tempExt[,2]))
       )

# identify locations where residuals are >100 or < -100
badResids_high <- predictionData %>%
  filter(resid > .5)  %>%
  terra::vect(geom = c("x", "y")) %>%
  terra::set.crs(crs("EPSG:4326")) %>%
  terra::project(crs(test_rast))
badResids_low <- predictionData %>%
  filter(resid < -.5)  %>%
  terra::vect(geom = c("x", "y")) %>%
  terra::set.crs(crs("EPSG:4326")) %>%
  terra::project(crs(test_rast)) 

# make figures
# make histogram
hist_i <- ggplot(predictionData) +
  geom_histogram(aes(resid_globMod), col = "darkgrey", fill = "lightgrey") +
  xlab(c("Residuals (obs. - pred.)"))
# make map
map_i <-  ggplot() +
geom_spatraster(data = plotObs_2) +
  geom_sf(data=cropped_states, fill=NA ) +
  geom_sf(data = badResids_high, col = "blue") +
  geom_sf(data = badResids_low, col = "red") +
labs(title = paste0("Residuals (obs. - pred.) for predictions of \n", holdoutRegion, " \n from a model fit to other ecoregions"),
     subtitle = paste0(response, " ~ ", paste0( modTerms, collapse = " + "))) +
  scale_fill_gradient2(low = "red",
                       mid = "white" ,
                       high = "blue" ,
                       midpoint = 0,   na.value = "grey20",
                       limits = c(-1, 1)) +
  xlim(c(min(tempExt[,1]), max(tempExt[,1]))) + 
  ylim(c(min(tempExt[,2]), max(tempExt[,2])))

 assign(paste0("residPlot_",holdoutRegion),
   value = ggarrange(map_i, hist_i, heights = c(3,1), ncol = 1)
)

}

  lapply(unique(modDat_1_s$NA_L2NAME), FUN = function(x) {
    get(paste0("residPlot_", x))
  })

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Using second best lambda model (either 1se or 1/2se)

Use terms from global model to re-fit and predict on different held out regions

Figures show residuals for each of the models fit to held-out ecoregions

These models were fit to six ecoregions, and then predict on the indicated heldout ecoregion

if (length(prednames_secondBestMod) == 0) {
  print("The model only contains one predictor (an intercept), so cross validation isn't practical")
} else {

## code from Tredennick et al. 2020
# try each separate level II ecoregion as a test set
# make a list to hold output data
outList <- vector(mode = "list", length = length(sort(unique(modDat_1_s$NA_L2NAME))))
# obs_pred <- data.frame(ecoregion = character(),obs = numeric(),
#                        pred_opt = numeric(), pred_null = numeric()#,
#                        #pred_nopenalty = numeric()
#                        )

## get the model specification from the global model
mat <- as.matrix(coef(mod_secondBest, s = "lambda.min"))
mat2 <- mat[mat[,1] != 0,]

f_cv <- as.formula(paste0(response, " ~ ", paste0(names(mat2)[2:length(names(mat2))], collapse = " + ")))

X_cv <- model.matrix(object = f_cv, data = modDat_1_s)
# get response variable
y_cv <- as.matrix(modDat_1_s[,response])


# now, loop through so with each iteration, a different ecoregion is held out
 for(i_eco in sort(unique(modDat_1_s$NA_L2NAME))){

  # split into training and test sets
  test_eco <- i_eco
  print(test_eco)
  # identify the rowID of observations to be in the training and test datasets
  train <- which(modDat_1_s$NA_L2NAME!=test_eco) # data for all ecoregions that aren't 'i_eco'
  test <- which(modDat_1_s$NA_L2NAME==test_eco) # data for the ecoregion that is 'i_eco'

  trainDat_all <- modDat_1_s %>%
    slice(train) %>%
    dplyr::select(-newRegion)
  testDat_all <- modDat_1_s %>%
    slice(test) %>%
    dplyr::select(-newRegion)

  # get the model matrices for input and response variables for cross validation model specification
  X_train <- as.matrix(X_cv[train,])
  X_test <- as.matrix(X_cv[test,])

  y_train <- modDat_1_s[train,response]
  y_test <- modDat_1_s[test,response]

  # get the model matrices for input and response variables for original model specification
  X_train_glob <- as.matrix(X[train,])
  X_test_glob <- as.matrix(X[test,])

  y_train_glob <- modDat_1_s[train,response]
  y_test_glob <- modDat_1_s[test,response]

  train_eco <- modDat_1_s$NA_L2NAME[train]

  ## just try a regular glm w/ the components from the global model
  fit_i <- glm(data = trainDat_all, formula = f_cv,
    ,
               family =  quasibeta_family(link = "logit")
    )

    coef(fit_i)

  # lasso model predictions with the optimal lambda
  optimal_pred <- predict(fit_i, newdata= testDat_all, type = "response") 
  # null model and predictions
  # the "null" model in this case is the global model
  # predict on the test data for this iteration w/ the global model
  null_pred <- predict.glm(mod_secondBest, newdata = testDat_all, type = "response") 

  # save data
  tmp <- data.frame(ecoRegion_holdout = rep(test_eco,length(y_test)),
                    obs=y_test,
                    pred_opt=optimal_pred,
                    pred_null=null_pred#,
                    #pred_nopenalty=nopen_pred
                    ) %>%
    cbind(testDat_all)

  # calculate RMSE, bias, etc. of
  # RMSE of CV model
  RMSE_optimal <- yardstick::rmse(data = data.frame(optimal_pred, "y_test" = (y_test)), truth = "y_test", estimate = "optimal_pred")[1,]$.estimate
  # RMSE of global model
  RMSE_null <- yardstick::rmse(data = data.frame(null_pred,  "y_test" = (y_test)), truth = "y_test", estimate = "null_pred")[1,]$.estimate
  # bias of CV model
  bias_optimal <- mean((y_test) - optimal_pred)
  # bias of global model
  bias_null <-  mean((y_test) - null_pred )

  # put output into a list
  tmpList <- list("testRegion" = i_eco,
    "modelObject" = fit_i,
       "modelPredictions" = tmp,
    "performanceMetrics" = data.frame("RMSE_cvModel" = RMSE_optimal,
                                      "RMSE_globalModel" = RMSE_null,
                                      "bias_cvModel" = bias_optimal,
                                      "bias_globalModel" = bias_null))

  # save model outputs
  outList[[which(sort(unique(modDat_1_s$NA_L2NAME)) == i_eco)]] <- tmpList
 }
}

## [1] "COLD DESERTS"
## [1] "MARINE WEST COAST FOREST"
## [1] "MEDITERRANEAN CALIFORNIA"
## [1] "MIXED WOOD PLAINS"
## [1] "MIXED WOOD SHIELD"
## [1] "SOUTH CENTRAL SEMIARID PRAIRIES"
## [1] "SOUTHEASTERN USA PLAINS AND EVERGLADES AND LOUISIANA PLAIN"
## [1] "TEMPERATE PRAIRIES"
## [1] "UPPER GILA MOUNTAINS"
## [1] "WARM DESERTS"
## [1] "WEST-CENTRAL SEMIARID PRAIRIES"
## [1] "WESTERN CORDILLERA"
## [1] "WESTERN SIERRA MADRE PIEDMONT"

Below are the RMSE and bias values for predictions made for each holdout level II ecoregion, compared to predictions from the global model for that same ecoregion

if (length(prednames_secondBestMod) == 0) {
  print("The model only contains one predictor (an intercept), so cross validation isn't practical")
} else {
# table of model performance
purrr::map(outList, .f = function(x) {
  cbind(data.frame("holdout region" = x$testRegion),  x$performanceMetrics)
}
) %>%
  purrr::list_rbind() %>%
  kable(col.names = c("Held-out ecoregion", "RMSE of CV model", "RMSE of global model",
                      "bias of CV model - mean(obs-pred.)", "bias of global model - mean(obs-pred.)"),
        caption = "Performance of Cross Validation using 'second best lambda' model specification") %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"))
}

Performance of Cross Validation using ‘second best lambda’ model specification

Held-out ecoregion	RMSE of CV model	RMSE of global model	bias of CV model - mean(obs-pred.)	bias of global model - mean(obs-pred.)
COLD DESERTS	0.1813783	0.1337148	-0.0966386	-0.0188312
MARINE WEST COAST FOREST	0.5251372	0.5241640	-0.4882175	-0.4871832
MEDITERRANEAN CALIFORNIA	0.2643383	0.1893875	0.1861681	0.0514793
MIXED WOOD PLAINS	0.3366784	0.3284174	-0.2841944	-0.2743685
MIXED WOOD SHIELD	0.3117854	0.3051259	0.0353456	0.0159007
SOUTH CENTRAL SEMIARID PRAIRIES	0.1693537	0.1349045	0.0724927	0.0151011
SOUTHEASTERN USA PLAINS AND EVERGLADES AND LOUISIANA PLAIN	0.2002998	0.1426958	0.0681253	0.0076524
TEMPERATE PRAIRIES	0.3204145	0.2299997	-0.2620689	-0.1435020
UPPER GILA MOUNTAINS	0.1522499	0.1510416	-0.0524542	-0.0493042
WARM DESERTS	0.1218842	0.1010825	-0.0391647	-0.0083018
WEST-CENTRAL SEMIARID PRAIRIES	0.1974418	0.1264084	0.1561799	0.0420277
WESTERN CORDILLERA	0.2358642	0.2170664	-0.0545461	-0.0433545
WESTERN SIERRA MADRE PIEDMONT	0.1536487	0.1442540	0.0995831	0.0861341

if (length(prednames_secondBestMod) == 0) {
  print("The model only contains one predictor (an intercept), so cross validation isn't practical")
} else {
for (i in 1:length(unique(modDat_1_s$NA_L2NAME))) {
  holdoutRegion <- outList[[i]]$testRegion
  predictionData <- outList[[i]]$modelPredictions
  modTerms <- as.matrix(coef(outList[[i]]$modelObject)) %>%
    as.data.frame() %>%
    filter(V1!=0) %>%
    rownames()

  # calculate residuals
  predictionData <- predictionData %>%
  mutate(resid = .[["obs"]] - .[["pred_opt"]] ,
         resid_globMod = .[["obs"]]  - .[["pred_null"]])

  # rasterize data
plotObs <- predictionData %>%
         drop_na(paste(response)) %>%
  #slice_sample(n = 5e4) %>%
  terra::vect(geom = c("x", "y")) %>%
  terra::set.crs(crs("EPSG:4326")) %>%
  terra::project(crs(test_rast)) %>% 
  terra::rasterize(y = test_rast,
                   field = "resid",
                   fun = mean) #%>%
  #terra::aggregate(fact = 2, fun = mean, na.rm = TRUE) %>%
  #terra::crop(ext(-1950000, 1000000, -1800000, 1000000))

tempExt <- crds(plotObs, na.rm = TRUE)

plotObs_2 <- plotObs %>%
  crop(ext(min(tempExt[,1]), max(tempExt[,1]),
           min(tempExt[,2]), max(tempExt[,2]))
       )

# identify locations where residuals are >100 or < -100
badResids_high <- predictionData %>%
  filter(resid > .5)  %>%
  terra::vect(geom = c("x", "y")) %>%
  terra::set.crs(crs("EPSG:4326")) %>%
  terra::project(crs(test_rast)) 
badResids_low <- predictionData %>%
  filter(resid < -.5)  %>%
  terra::vect(geom = c("x", "y")) %>% 
  terra::set.crs(crs("EPSG:4326")) %>%
  terra::project(crs(test_rast)) 


# make figures
# make histogram
hist_i <- ggplot(predictionData) +
  geom_histogram(aes(resid_globMod), col = "darkgrey", fill = "lightgrey") +
  xlab(c("Residuals (obs. - pred.)"))
# make map
map_i <-  ggplot() +
geom_spatraster(data = plotObs_2) +
  geom_sf(data=cropped_states,fill=NA ) +
  geom_sf(data = badResids_high, col = "blue") +
  geom_sf(data = badResids_low, col = "red") +
labs(title = paste0("Residuals (obs. - pred.) for predictions of \n", holdoutRegion, " \n from a model fit to other ecoregions"),
     subtitle = paste0(response, " ~ ", paste0( modTerms, collapse = " + "))) +
  scale_fill_gradient2(low = "red",
                       mid = "white" ,
                       high = "blue" ,
                       midpoint = 0,   na.value = "grey20",
                       limits = c(-1, 1))  +
  xlim(st_bbox(plotObs_2)[c(1,3)]) +
  ylim(st_bbox(plotObs_2)[c(2,4)])

 assign(paste0("residPlot_",holdoutRegion),
   value = ggarrange(map_i, hist_i, heights = c(3,1), ncol = 1)
)

}

  lapply(unique(modDat_1_s$NA_L2NAME), FUN = function(x) {
    get(paste0("residPlot_", x))
  })
}

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Save output

## save the coefficients for the models (best lambda, 1/2se lambda, 1se lambda)
if(trimAnom == TRUE) {
saveRDS(coefs, file = paste0("./models/modelCoefficients_trimAnom_", ecoregion, "_", response,"_removeAnomalies", removeAllAnoms,".rds"))
saveRDS(uniqueCoeffs, file = paste0("./models/modelMetrics_trimAnom_", ecoregion, "_", response,"_removeAnomalies", removeAllAnoms,".rds"))
} else {
saveRDS(coefs, file = paste0("./models/modelCoefficients_", ecoregion, "_", response,"_removeAnomalies", removeAllAnoms,".rds"))
saveRDS(uniqueCoeffs, file = paste0("./models/modelMetrics_", ecoregion, "_", response,"_removeAnomalies", removeAllAnoms,".rds"))
}
# make a table

## partial dependence plots
#vip::vip(mod_glmFinal, num_features = 15)

#pdp_all_vars(mod_glmFinal, mod_vars = pred_vars, ylab = 'probability',train = df_small)

#caret::varImp(fit)

session info

Hash of current commit (i.e. to ID the version of the code used)

system("git rev-parse HEAD", intern=TRUE)

## [1] "95e228db41b746742f867818bc949f28170da54a"

Packages etc.

sessionInfo()

## R version 4.5.2 (2025-10-31)
## Platform: aarch64-apple-darwin20
## Running under: macOS Tahoe 26.2
## 
## Matrix products: default
## BLAS:   /System/Library/Frameworks/Accelerate.framework/Versions/A/Frameworks/vecLib.framework/Versions/A/libBLAS.dylib 
## LAPACK: /Library/Frameworks/R.framework/Versions/4.5-arm64/Resources/lib/libRlapack.dylib;  LAPACK version 3.12.1
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## time zone: America/Denver
## tzcode source: internal
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] ggpubr_0.6.2               factoextra_1.0.7          
##  [3] USA.state.boundaries_1.0.1 glmnet_4.1-10             
##  [5] Matrix_1.7-4               kableExtra_1.4.0          
##  [7] rsample_1.3.2              here_1.0.2                
##  [9] StepBeta_2.1.0             ggtext_0.1.2              
## [11] gridExtra_2.3              pdp_0.8.3                 
## [13] GGally_2.4.0               lubridate_1.9.4           
## [15] forcats_1.0.1              stringr_1.6.0             
## [17] dplyr_1.2.0                purrr_1.2.1               
## [19] readr_2.1.6                tidyr_1.3.2               
## [21] tibble_3.3.1               tidyverse_2.0.0           
## [23] caret_7.0-1                lattice_0.22-7            
## [25] ggplot2_4.0.2              sf_1.0-24                 
## [27] tidyterra_1.0.0            terra_1.8-93              
## [29] ggspatial_1.1.10           betareg_3.2-4             
## [31] dtplyr_1.3.2               patchwork_1.3.2           
## 
## loaded via a namespace (and not attached):
##   [1] RColorBrewer_1.1-3   rstudioapi_0.18.0    jsonlite_2.0.0      
##   [4] shape_1.4.6.1        magrittr_2.0.4       modeltools_0.2-24   
##   [7] farver_2.1.2         rmarkdown_2.30       vctrs_0.7.1         
##  [10] rstatix_0.7.3        htmltools_0.5.9      broom_1.0.12        
##  [13] Formula_1.2-5        pROC_1.19.0.1        sass_0.4.10         
##  [16] parallelly_1.46.1    KernSmooth_2.23-26   bslib_0.10.0        
##  [19] plyr_1.8.9           sandwich_3.1-1       zoo_1.8-15          
##  [22] cachem_1.1.0         commonmark_2.0.0     lifecycle_1.0.5     
##  [25] iterators_1.0.14     pkgconfig_2.0.3      R6_2.6.1            
##  [28] fastmap_1.2.0        future_1.69.0        digest_0.6.39       
##  [31] furrr_0.3.1          rprojroot_2.1.1      textshaping_1.0.4   
##  [34] labeling_0.4.3       yardstick_1.3.2      timechange_0.4.0    
##  [37] mgcv_1.9-4           abind_1.4-8          compiler_4.5.2      
##  [40] proxy_0.4-29         aod_1.3.3            withr_3.0.2         
##  [43] S7_0.2.1             backports_1.5.0      carData_3.0-6       
##  [46] DBI_1.2.3            ggstats_0.12.0       ggsignif_0.6.4      
##  [49] MASS_7.3-65          lava_1.8.2           classInt_0.4-11     
##  [52] gtools_3.9.5         ModelMetrics_1.2.2.2 tools_4.5.2         
##  [55] units_1.0-0          lmtest_0.9-40        otel_0.2.0          
##  [58] future.apply_1.20.1  nnet_7.3-20          glue_1.8.0          
##  [61] nlme_3.1-168         gridtext_0.1.5       grid_4.5.2          
##  [64] reshape2_1.4.5       generics_0.1.4       recipes_1.3.1       
##  [67] gtable_0.3.6         tzdb_0.5.0           class_7.3-23        
##  [70] data.table_1.18.2.1  hms_1.1.4            car_3.1-5           
##  [73] xml2_1.5.2           flexmix_2.3-20       markdown_2.0        
##  [76] ggrepel_0.9.6        foreach_1.5.2        pillar_1.11.1       
##  [79] splines_4.5.2        survival_3.8-6       tidyselect_1.2.1    
##  [82] knitr_1.51           litedown_0.9         svglite_2.2.2       
##  [85] stats4_4.5.2         xfun_0.56            hardhat_1.4.2       
##  [88] timeDate_4052.112    stringi_1.8.7        yaml_2.3.12         
##  [91] evaluate_1.0.5       codetools_0.2-20     cli_3.6.5           
##  [94] rpart_4.1.24         systemfonts_1.3.1    jquerylib_0.1.4     
##  [97] Rcpp_1.1.1           globals_0.19.0       parallel_4.5.2      
## [100] gower_1.0.2          listenv_0.10.0       viridisLite_0.4.2   
## [103] ipred_0.9-15         scales_1.4.0         prodlim_2025.04.28  
## [106] e1071_1.7-17         combinat_0.0-8       rlang_1.1.7         
## [109] cowplot_1.2.0